Question

1) Find the sum S of the series where S = Σ i ai -- here...

1) Find the sum S of the series where S = Σ i ai -- here i varies from 1 to n.


Use the mathematical induction to prove the following:
2) 13 + 33 + 53 + …. + (2n-1)3 = n2(2n2-1)
3) Show that n! > 2n for all n > 3.
4) Show that 9(9n -1) – 8n is divisible by 64.


Show all the steps and calculations for each of the above and explain your answer in detail.

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