Telescoping Series ,Showing Divergence Using Partial Sums

Telescoping Series ,Showing Divergence Using Partial Sums. Here I find a formula for a partial sum of a geometric series and show that the series diverges.

Category:

Education

Tags:

• telescoping
• series
• partial
• sum
• diverge
• calculus
• limit

[viczhou11]

@Zuzu9328

Thank you!

[Zuzu9328]

@viczhou11 Look at n = 3 since that's where things start to cancel. You're left with ln(4) and ln(5) but you can tell by intuition that those will cancel later. So you generalize for the partial sum ln(k+1) and ln(k+2) since where ever you stop will still have those two terms.

[viczhou11]

I do not quite understand where you get ln(k+1) and ln(k+2). Where do you start counting k? from which term?

[aarontheedge07]

@beautifulshapley I'm watching this with an exam in an hour haha

[beautifulshapley]

Thanks alot! I have an exam in two days T_T! This is a big help!