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Show by the Principle of Mathematical induction that the sum `S_n`, of the nterms of the series `1^2 + 2xx 2^2 + 3^2 + 2xx 4^2+5^2 +2 xx 6^2 +7^2+..... ` is given by `S_n={(n(n+1)^2)/2`, if n is even , then `(n^2(n+1))/2` , if n is odd

A

`S_n=(n(n+1)^2)/2` , If n is even

B

`S_n=(n^2(n+1))/2`, if n is odd

C

Both (a) and (b) are true

D

Both (a) and (b) are false

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The correct Answer is:
C
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DISHA PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-Exercise-2 Concept Applicator
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  14. If n is a positive integer, then 2.4^(2n+1)+3^(3n+1) is divisible by :

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  18. If n is any odd number greater than 1, then n\ (n^2-1) is divisible b...

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