Thread: Finite sum sequence--help please!

Given the following finite sum
1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+....+1/(n(n+1))

a) Find the first 5 partial sums
b) Make a conjecture for a formula for the sum of the first n terms
c) Use mathematical induction to prove your formula

Originally Posted by sensuji

Given the following finite sum
1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+....+1/(n(n+1))

a) Find the first 5 partial sums
b) Make a conjecture for a formula for the sum of the first n terms
c) Use mathematical induction to prove your formula

a) You can do.

b)

c) Do you know what induction is?

Prove base case. I.e. show for n=1,

Assume true for n.

Prove for n+1. Hint,

isn't there a prove that n=k step or something like that?

Originally Posted by sensuji

isn't there a prove that n=k step or something like that?

No you assume its true for n=k then prove it for n=k+1.

http://en.wikipedia.org/wiki/Mathematical_induction