# Free Calc Solutions

**How do they get from step 2 to three in this CALC question?**

go here http://calcchat.tdlc.com/free_solutions/main.html

the textbook is calculus, 8th edition chapter 9, section 2, exercise 23. How do they get Sn??

lol i think i just figured it out, is it because every number after 1 up to n is canceled out?

It’s what’s called a ‘telescoping series’. All the terms but the first and last cancel. It might help to work out the first few to see the pattern:

S1 = 1 – 1/2

S2 = 1 – 1/2 + 1/2 – 1/3 = 1 – 1/3

S3 = 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 = 1 – 1/4

and so on…

Edit: You got it 🙂

**2002 AP calculus free response — areas and volumes**