Given expression, p(n)=2.42n+1+33n+1 Let n=1 p(1)=2.42+1+33+1=209 which is divisible by 11. Let p(k) is also divisible by 11. p(k)=2.42k+1+33k+1 is divisibly by 11 ...(i) Now we will prove that p(k+1) is true. p(k+1)=2.42k+1)+1+33k+11+1 =2.42k+1.16+33k+1.27 =2.42k+1.16+33k+1.16+33k+1.11 =16(2.42k+1+33k+1)+33k+1.11 Divisible by 11 from Eq. (i) ∴p(k+1) is also true. ∴p(n) is divisible by 11 .