Statement 1: For every natural number n ≥ 2, 11+12+…+1n>n ,Statement  2: For every natural number n ≥ 2, n(n+1)

P(n)=11+12+…+1nP(2)=11+12>2Let us assume that P(k)=11+12+…+1k>k is true.∴ P(k+1)=11+12+…+1k+1k+1>k+1 has to be true . L.H.S. >k+1k+1=k(k+1)+1k+1 sincek(k+1)>k(∀k≥0)∴ k(k+1)+1k+1>k+1k+1=k+1Let P(n)=n(n+1)