Question

1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}_________________________________________________(a) n(n + 1)(b) n/(n + 1)(c) 2n/(n + 1)(d) 3n/(n + 1) *​

Answer 1

Answer:

Explanation:

Induction method is used to prove a statement. Most commonly, it is used to prove a statement, involving, say n where n represents the set of all natural numbers.

Induction method involves two steps, One, that the statement is true for n=1 and say n=2. Two, we assume that it is true for n=k and prove that if it is true for n=k, then it is also true for n=k+1.

First Step − Now for 11⋅2+12⋅3+...+1n(n+1)=nn+1, we know for n=1, we have 11⋅2=12 and for n=2, we have 11⋅2+12⋅3=12+16=23=22+1.

Hence, given statement is true for n=1 and n=2.

Second Step − Assume it is true for n=k, hence

11⋅2+12⋅3+...+1k(k+1)=kk+1

Now let us test it for 

Answer 2

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