Question

Prove by method of induction, for all n ∈ N 1/1.3+1/3.5+1/5.7 + .... 1/(2n-1)(2n+1) = n/2n+1

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Answer:

Hence it is proved by PMI that both sides are equal.

Step-by-step explanation:

Step 1: Given data. P(n) : 1/1.3+1/3.5+−−−−−+1/(2n−1)(2n+1)

=n/(2n+1)

Step 2: To prove, P(1) is true.

LHS=1/1.3=1/3.

RHS=1/2×1+1=1/3.

Thus, P(1) is true.

⇒LHS=RHS

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