Me possibly overthinking a geometric series question
up vote
0
down vote
favorite
I am creating a study sheet for geometric series and came across this questions
Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as well as explain how you get this infinite geometric series. If not, explain why.
This is possible with some neagitve common ratio, r, where $|r|<1$ correct?
geometric-series
asked Dec 4 at 0:31
K Math
59529
add a comment |
up vote
0
down vote
favorite
I am creating a study sheet for geometric series and came across this questions
Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as well as explain how you get this infinite geometric series. If not, explain why.
This is possible with some neagitve common ratio, r, where $|r|<1$ correct?
geometric-series
asked Dec 4 at 0:31
K Math
59529
What have you tried so far? What $r$ do you have in mind?
– platty
Dec 4 at 0:33
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am creating a study sheet for geometric series and came across this questions
Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as well as explain how you get this infinite geometric series. If not, explain why.
This is possible with some neagitve common ratio, r, where $|r|<1$ correct?
geometric-series
asked Dec 4 at 0:31
K Math
59529
I am creating a study sheet for geometric series and came across this questions
Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as well as explain how you get this infinite geometric series. If not, explain why.
This is possible with some neagitve common ratio, r, where $|r|<1$ correct?
geometric-series
geometric-series
asked Dec 4 at 0:31
K Math
59529
asked Dec 4 at 0:31
K Math
59529
asked Dec 4 at 0:31
K Math
59529
asked Dec 4 at 0:31
K Math
59529
asked Dec 4 at 0:31
K Math
59529
59529
What have you tried so far? What $r$ do you have in mind?
– platty
Dec 4 at 0:33
add a comment |
What have you tried so far? What $r$ do you have in mind?
– platty
Dec 4 at 0:33
What have you tried so far? What $r$ do you have in mind?
– platty
Dec 4 at 0:33
What have you tried so far? What $r$ do you have in mind?
– platty
Dec 4 at 0:33
add a comment |
1 Answer
1
active
oldest
votes
up vote
3
down vote
You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.
answered Dec 4 at 0:34
Frpzzd
20.8k638104
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
– K Math
Dec 4 at 0:43
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.
answered Dec 4 at 0:34
Frpzzd
20.8k638104
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
– K Math
Dec 4 at 0:43
add a comment |
up vote
3
down vote
You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.
answered Dec 4 at 0:34
Frpzzd
20.8k638104
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
– K Math
Dec 4 at 0:43
add a comment |
up vote
3
down vote
up vote
3
down vote
You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.
answered Dec 4 at 0:34
Frpzzd
20.8k638104
You know that if $a$ is the first term of a geometric series and $r$ is the ratio, then the sum is given by
$$S=sum_{n=0}^infty ar^n=frac{a}{1-r}$$
So, if $a=10$ and $S=4$, then
$$frac{10}{1-r}=4implies r=-frac{3}{2}$$
but the series does not converge in this case, so the solution is extraneous and the described situation is not possible.
answered Dec 4 at 0:34
Frpzzd
20.8k638104
answered Dec 4 at 0:34
Frpzzd
20.8k638104
answered Dec 4 at 0:34
Frpzzd
20.8k638104
answered Dec 4 at 0:34
Frpzzd
20.8k638104
20.8k638104
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
– K Math
Dec 4 at 0:43
add a comment |
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
– K Math
Dec 4 at 0:43
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
– K Math
Dec 4 at 0:43
ok this is what I continued to get when I was solving but wasn't sure if I was missing something.
– K Math
Dec 4 at 0:43
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3024936%2fme-possibly-overthinking-a-geometric-series-question%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
What have you tried so far? What $r$ do you have in mind?
– platty
Dec 4 at 0:33