Question

Infinite Series
Can anyone tell me how they came to that last form on the second line of this solution?

http://calcchat.tdlc.com/calcchat/printsolution.jsp?roomName=Calculus%20ETF%205e%209.2%20Ex%2043&artName=se09b01043.png&chapFolder=09&secFolder=b&solutionPath=http://calcchat.tdlc.com/solutionart/etf5e/

Answer 1

your link got chopped ....

Answer 2

look up "screen shot" on google if you need help showing your stuff

Answer 3

telescoping sum

Answer 4

If you have a look every term after 1/2 is canceled except for the last one, -1/3 + 1/3, - 1/4 + 1/4, etc.

Answer 5

What you end up with is 1/2 - 1/n+2

Answer 6

Then obviously you take the limit and the 1/n+2 disappears

Answer 7

i know you have the answer, but i just love saying "TELESCOPING SUM" don't you?

Answer 8

Oh sure, its like looking through a telescope and all you see is the last term.

Answer 9

I honestly don't know if that's where the term comes from.

Answer 10

It is a nice term

Answer 11

because it telescopes! looks like
============================================
but then collapses to
==

Answer 12

ooh I see yeah that makes sense.

Answer 13

i guess "un-telescopes" might be more descriptive

Answer 14

I guess I forgot that there are those small handheld telescopes that fold up.

Answer 15

If there is one area I am weak in it is the history of mathematics. I don't know the origin of the term.

Answer 16

There are some very interesting people in the history of mathematics. Its probably worth studying if you are interested in how things evolved.

Answer 17

As a full time professor I really don't have the time to do that ;)

Answer 18

Ah but you have time to answer questions here. I'm calling your bluff :P

Answer 19

I'm also really lazy. :) I don't want to read the history of math and I'm done taking classes