By experimenting with small values of n guess a formula for

By experimenting with small values of n, guess a formula for the given sum, 1/1*2 + 1/2*3 + ..... + 1/n*(n+1), then use induction to verify your formula

my formula is 1/1*2 + 1/2*3 + ..... + 1/n*(n+1=n/n+1

Solution

Let us prove for n=1,

P(n) = 1/1+1

=1/2

It is true for n=1

Let P(k) is true

P(k): k/k+1

We have to prove that P(k+1) is true

P(k+1): (k/k+1)+(k+1/k+2)

Hence like this we can prove that P(k+1) is true...