Consider the statement
`P(n):1^2+2^2+3^2+…….+n^2-(n(n+1)(2n+1))/6`
By assume that `P(k)` is true, prove that `P(k+1)` is true.

Consider the statement P(n):1^2+2^2+3^2+…….+n^2=(n(n+1)(2n+1))/6 Check whether P(1) is true.

Consider the statement P(n):1x2+2x3+3x4+………+n(n+1)='(n(n+1)(n+2)/3' (a)Verify that P(3) is true.

Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 If P(k) is true, prove that P(k+1) is true.

Consider the statement P(n):1.2+2.3+3.4+…….+n(n+1)=(n(n+1)(n+2))/3 Prove that P(1) is true.

Consider the statement P(n):1.2+2.3+3.4+…….+n(n+1)=(n(n+1)(n+2))/3 Assume that P(k) is true for a natural number k, verify that P(k+1) is true.

Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 Prove that P(1) is true.

Consider the statement P(n)=1+3+3^2+….+3^(n-1)=(3^n-1)/2 (b)If P(k) is true,prove that P(k+1) is also true.

Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n)-1)(2) If P(k) is true, prove that P(k+1) is true.

Consider the statement P(n):1^2+2^2+3^2+…….+n^2=(n(n+1)(2n+1))/6 Is P(n) true for all natural number n? Justify your answer.

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assume that P(k) is true for a natural number k, Verify that P(k+1) is true.