Problem Statement:
Using Mathematical Induction, prove that for n > 1,
Mathematical Proof:
First of all, we will prove for the base case n=2.
LHS =
RHS =
Both LHS and RHS ( Left hand side and Right hand side ) are equal. So its is proved for the base case.
Let us assume that for P(k) for k ≥ 2 be a arbitrarily chosen integer such that the equation holds true.
Using that we prove that for P(k+1) , the equation holds true, such that :
Let us multiply the k+1 term using the P(k) , we get:
Simplify and get to the form of P(k+1)
Expand the RHS and get to the form of p(k+1), we get
RHS = %5E%7B2%7D%7D)
= %7D)
= 
%5E2&space;-1%7D%7B2k(k+1)%7D)
= %7D)
Cancel the k, we get
= %7D)
= +1%7D%7B2(k+1)%7D)
We proved for the P(k+1) using the P(k)
Hence proved that:
