Question

Compute the sum of (1/k)-(1/(k+1)) from k=1 to n?

Answer 1

@iambatman

Answer 2

I understand that it has something to do with telescoping series but I'm not sure how it applies here

Answer 3

\[\sum_{k=1}^{n} \left( \frac{ 1 }{ k }-\frac{ 1 }{ (k+1) } \right)\] like this?

Answer 4

Yeah, that's what it's asking for

Answer 5

Well for telescoping first thing you want to do is plug in a few numbers and see what's going on, so try that, and then look for which terms cancel each other out.

Answer 6

After 1, it seems every term after cancels out
\[1-\frac{ 1 }{ 2 } + \frac{ 1 }{ 2 }-\frac{ 1 }{ 3 }+\frac{ 1 }{ 3 }-\frac{ 1 }{ 4 }+...\]

Answer 7

Yeah so you're on the right track 1 is going to stay, but what is the nth term?

Answer 8

I assume it would be
\[\frac{ 1 }{ n }-\frac{ 1 }{ n+1 }\]

Answer 9

Yes, so 1/n would eventually get cancelled out, so you'll be left with?

Answer 10

I would be left with \[\frac{ 1 }{ n +1}\] if it were to get canceled out

Answer 11

Remember the 1? It never got cancelled out, so you would actually have \[1-\frac{ 1 }{ n+1 }\]

Answer 12

So say n was equal to some number, if I plug it into this it would give the sum?

Answer 13

Yes, so this is your sum unless it was asking for convergence/ divergence then you would have to take the limit.

Answer 14

It didn't ask for convergence/divergence so I assume this is what the problem wants

Answer 15

You're good then ^.^