Q. 16

Prove the followi

Answer :

Let P(n): 2 + 5 + 8 + 11 + … + (3n – 1) = n(3n + 1)


For n=1


P(1): 2 = .1.(4)


2 = 2


Since, P(n) is true for n = 1


Let P(n) is true for n = k, so


P(k): 2 + 5 + 8 + 11 + … + (3k – 1) = k(3k + 1) - - - - - - - (1)


We have to show that,


2 + 5 + 8 + 11 + … + (3k – 1) + (3k + 2) = (k + 1)(3k + 4)


Now,


{2 + 5 + 8 + 11 + … + (3k – 1)} + (3k + 2)


= .k(3k + 1) + (3k + 2)


=


=


=


=


=


=


Therefore, P(n) is true for n = k + 1


Hence, P(n) is true for all n N by PMI

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