Question

Hey mates
Can u pls answer the 1st one
Asap

Answer 1

step 1:verify the result for n=2, 1-1/2^2=1-1/4=3/4=2+1/2^2=3/4. step 2:let us assume that the result is true for n=k, (1-1/2^2)(1-1/3^2)..............(1-1/n^2)=n+1/2n. step 3:we shall prove that the result is true for n=k+1. (1-1/2^2)(1-1/3^2)..........(1-1/k^2)(1-1/k+1^2)=k+1+1/2(k+1). LHS n+1/2n (1-1/k+1^2=RHS