Sum $frac{1}{1×2} + frac{1}{2×3} + …+frac{1}{(n-1)n}$ [on hold]
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What is the sum $S_n$ of such sequence:
$frac{1}{1×2} + frac{1}{2×3} + ...+frac{1}{(n-1)n}$
I tried but couldn't get it.
sequences-and-series
edited Dec 1 at 13:00
Arjang
5,55162363
asked Dec 1 at 4:43
J.Moh
395
put on hold as off-topic by user302797, Martin Sleziak, Cesareo, Arjang, Did Dec 1 at 17:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, Cesareo, Arjang, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
What is the sum $S_n$ of such sequence:
$frac{1}{1×2} + frac{1}{2×3} + ...+frac{1}{(n-1)n}$
I tried but couldn't get it.
sequences-and-series
edited Dec 1 at 13:00
Arjang
5,55162363
asked Dec 1 at 4:43
J.Moh
395
put on hold as off-topic by user302797, Martin Sleziak, Cesareo, Arjang, Did Dec 1 at 17:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, Cesareo, Arjang, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
4
Possible Duplicate of this
– Mason
Dec 1 at 4:47
+ This is not an arithmetic sequence. Here may be a helpful intro to that: khanacademy.org/math/algebra/sequences/…
– Mason
Dec 1 at 4:52
Possible duplicate of What is the formula for $frac{1}{1cdot 2}+frac{1}{2cdot 3}+frac{1}{3cdot 4}+cdots +frac{1}{n(n+1)}$
– Martin Sleziak
Dec 1 at 7:29
hint: $frac{1}{k(k+1)} = frac{1}{k} - frac{1}{k+1}$
– Student
Dec 1 at 13:04
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What is the sum $S_n$ of such sequence:
$frac{1}{1×2} + frac{1}{2×3} + ...+frac{1}{(n-1)n}$
I tried but couldn't get it.
sequences-and-series
edited Dec 1 at 13:00
Arjang
5,55162363
asked Dec 1 at 4:43
J.Moh
395
What is the sum $S_n$ of such sequence:
$frac{1}{1×2} + frac{1}{2×3} + ...+frac{1}{(n-1)n}$
I tried but couldn't get it.
sequences-and-series
sequences-and-series
edited Dec 1 at 13:00
Arjang
5,55162363
asked Dec 1 at 4:43
J.Moh
395
edited Dec 1 at 13:00
Arjang
5,55162363
asked Dec 1 at 4:43
J.Moh
395
edited Dec 1 at 13:00
Arjang
5,55162363
edited Dec 1 at 13:00
Arjang
5,55162363
edited Dec 1 at 13:00
Arjang
5,55162363
5,55162363
asked Dec 1 at 4:43
J.Moh
395
asked Dec 1 at 4:43
J.Moh
395
asked Dec 1 at 4:43
J.Moh
395
395
put on hold as off-topic by user302797, Martin Sleziak, Cesareo, Arjang, Did Dec 1 at 17:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, Cesareo, Arjang, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by user302797, Martin Sleziak, Cesareo, Arjang, Did Dec 1 at 17:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, Cesareo, Arjang, Did
If this question can be reworded to fit the rules in the help center, please edit the question.
4
Possible Duplicate of this
– Mason
Dec 1 at 4:47
+ This is not an arithmetic sequence. Here may be a helpful intro to that: khanacademy.org/math/algebra/sequences/…
– Mason
Dec 1 at 4:52
Possible duplicate of What is the formula for $frac{1}{1cdot 2}+frac{1}{2cdot 3}+frac{1}{3cdot 4}+cdots +frac{1}{n(n+1)}$
– Martin Sleziak
Dec 1 at 7:29
hint: $frac{1}{k(k+1)} = frac{1}{k} - frac{1}{k+1}$
– Student
Dec 1 at 13:04
add a comment |
4
Possible Duplicate of this
– Mason
Dec 1 at 4:47
+ This is not an arithmetic sequence. Here may be a helpful intro to that: khanacademy.org/math/algebra/sequences/…
– Mason
Dec 1 at 4:52
Possible duplicate of What is the formula for $frac{1}{1cdot 2}+frac{1}{2cdot 3}+frac{1}{3cdot 4}+cdots +frac{1}{n(n+1)}$
– Martin Sleziak
Dec 1 at 7:29
hint: $frac{1}{k(k+1)} = frac{1}{k} - frac{1}{k+1}$
– Student
Dec 1 at 13:04
4
4
Possible Duplicate of this
– Mason
Dec 1 at 4:47
Possible Duplicate of this
– Mason
Dec 1 at 4:47
+ This is not an arithmetic sequence. Here may be a helpful intro to that: khanacademy.org/math/algebra/sequences/…
– Mason
Dec 1 at 4:52
+ This is not an arithmetic sequence. Here may be a helpful intro to that: khanacademy.org/math/algebra/sequences/…
– Mason
Dec 1 at 4:52
Possible duplicate of What is the formula for $frac{1}{1cdot 2}+frac{1}{2cdot 3}+frac{1}{3cdot 4}+cdots +frac{1}{n(n+1)}$
– Martin Sleziak
Dec 1 at 7:29
Possible duplicate of What is the formula for $frac{1}{1cdot 2}+frac{1}{2cdot 3}+frac{1}{3cdot 4}+cdots +frac{1}{n(n+1)}$
– Martin Sleziak
Dec 1 at 7:29
hint: $frac{1}{k(k+1)} = frac{1}{k} - frac{1}{k+1}$
– Student
Dec 1 at 13:04
hint: $frac{1}{k(k+1)} = frac{1}{k} - frac{1}{k+1}$
– Student
Dec 1 at 13:04
add a comment |
1 Answer
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Hint:$$sum_{n=1}^{infty} {1over n(n+1)}=sum_{n=1}^{infty} {1over n}-{1over n+1}$$
answered Dec 1 at 14:05
Mostafa Ayaz
13.3k3836
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Hint:$$sum_{n=1}^{infty} {1over n(n+1)}=sum_{n=1}^{infty} {1over n}-{1over n+1}$$
answered Dec 1 at 14:05
Mostafa Ayaz
13.3k3836
add a comment |
up vote
1
down vote
Hint:$$sum_{n=1}^{infty} {1over n(n+1)}=sum_{n=1}^{infty} {1over n}-{1over n+1}$$
answered Dec 1 at 14:05
Mostafa Ayaz
13.3k3836
add a comment |
up vote
1
down vote
up vote
1
down vote
Hint:$$sum_{n=1}^{infty} {1over n(n+1)}=sum_{n=1}^{infty} {1over n}-{1over n+1}$$
answered Dec 1 at 14:05
Mostafa Ayaz
13.3k3836
Hint:$$sum_{n=1}^{infty} {1over n(n+1)}=sum_{n=1}^{infty} {1over n}-{1over n+1}$$
answered Dec 1 at 14:05
Mostafa Ayaz
13.3k3836
answered Dec 1 at 14:05
Mostafa Ayaz
13.3k3836
answered Dec 1 at 14:05
Mostafa Ayaz
13.3k3836
answered Dec 1 at 14:05
Mostafa Ayaz
13.3k3836
13.3k3836
add a comment |
add a comment |
4
Possible Duplicate of this
– Mason
Dec 1 at 4:47
+ This is not an arithmetic sequence. Here may be a helpful intro to that: khanacademy.org/math/algebra/sequences/…
– Mason
Dec 1 at 4:52
Possible duplicate of What is the formula for $frac{1}{1cdot 2}+frac{1}{2cdot 3}+frac{1}{3cdot 4}+cdots +frac{1}{n(n+1)}$
– Martin Sleziak
Dec 1 at 7:29
hint: $frac{1}{k(k+1)} = frac{1}{k} - frac{1}{k+1}$
– Student
Dec 1 at 13:04