question_answer 1)

If , then prove that An =  where n is any positive integer.  

Answer:

We shall prove it by the principle of Mathematical Induction.       For n = 1,       which is true.        given statement is true for n = 1.       Let us suppose that given statement is true for n = k.             ?? (1)       Consider for n = k + 1                               which is true for n = k + 1        by P.M.I., it is a true for every positive integer k.