Answer :

P(1) is true

Let P (k) be true

1.3 + 3.5 + 5.7 +… + (2k –1) (2k + 1) =

To prove p(k+1) is true using P(k) lies

1.3 + 3.5 + 5.7 +… + (2k –1) (2k + 1)+[2(k+1)-1] [2(k+1)+1]

=

=

=

= ……….(1)

=

=

L. H.S of (1)

1.3 + 3.5 + 5.7 +… + (2k –1) (2k + 1)+[2(k+1)-1] [2(k+1)+1]

=

=

=

=

=

Which is the R. H.s of (1)

P(K+1) is true.

By the Principle of mathematical induction, P(n) is true for all values of n where n N

Hence proved.

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