Prove 1- 1 1 1- 1 2 1- 1 3 - 1- 1 n - n-1 -

( 1 + 11)( 1 + 12)( 1 + 13)...( 1 + 1n) Here #160; #160; a_n = 1 + 1n = n + 1n Therefore, #160; ( 1 + 11)( 1 + 12)( 1 + 13)...( 1 + 1n ...

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Summation by Sigma Method

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Question

Prove $(1 + \frac{1}{1}) (1 + \frac{1}{2}) (1 + \frac{1}{3}) . . . (1 + \frac{1}{n}) = (n + 1) .$

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Prove $(1 + \frac{1}{1}) (1 + \frac{1}{2}) (1 + \frac{1}{3}) \dots (1 + \frac{1}{n}) = (n + 1) .$

n \in N : (1 + \frac{1}{1}) (1 + \frac{1}{2}) (1 + \frac{1}{3}) . . . . . . (1 + \frac{1}{n}) = (n + 1)

Prove the following by using the principle of mathematical induction for all n ∈ N:

n \in N

(1 + \frac{1}{1}) (1 + \frac{1}{2}) (1 + \frac{1}{3}) \dots (1 + \frac{1}{n}) = (n + 1)

Value of (1/2)(1-1/3).......(1-1/n-1)(1-1/n)

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