Prove by method of induction, for all n €N.
(1) 2+4 +6 + ..... + 2n = n(n+1)
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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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