Free Calc Solutions

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

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