question: find out if the following converges and if it does find what number it converges to: use a telescoping sum
work: I used partial fractions to get
then I used a telescoping sum and the first term and last term remained, which are and then taking the limit n-->infinity I'm left with 1/2.
Is this right? When I graphed the function it appears to go to 1.
I see where I went wrong: I wrote out 3 terms and thought that all but the first and last number would cancel out in the sequence
e.g.
how do I make sure that I don't make the same mistake in the future, I mean I can't write out infinitely many terms and I thought 3 would be sufficent to see the pattern. I mean isn't it pretty tricky when 1 term in the middle doesn't cancel out?
I am unclear as to what you mean. I thought the first and last term remained and the rest canceled out.
what's in blue is what I thought canceled.