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  • Match the questions given under Column I with their appropriate answers given under the Column II. a)1^2+2^2+...+n^2 i)[n(n+1)/2]^2

Match the questions given under Column I with their appropriate answers given under the Column II.

 

Column-I Column-II
a)1^{2}+2^{2}+3^{2}+\ldots+n^{2} i)\left(\frac{n(n+1)}{2}\right)^{2}
b)1^{3}+2^{3}+3^{3}+\ldots+n^{3} ii)n(n+1)
c)2+4+6+...+2n iii)\frac{n(n+1)(2 n+1)}{6}
d)1+2+3+...+n iv)\frac{n(n+1)}{2}

 

Answers (1)

Sum of ‘n’ natural numbers    \sum _{i=1}^{n}i= \left( \frac{n \left( n+1 \right) }{2} \right) \\\\

Sum of cube of ‘n’ natural numbers  \sum _{i=1}^{n}i^{3}= \left( \frac{n \left( n+1 \right) }{2} \right) ^{2} \\\\

Sum of square of ‘n’ natural numbers   \sum _{i=1}^{n}i^{2}= \left( \frac{n \left( n+1 \right) \left( 2n+1 \right) }{6} \right) \\\\

Sum of twice times ‘n’ natural numbers  \sum _{i=1}^{n}2i=n \left( n+1 \right) \\\\

So, (a) – (iii), (b)- (i), (c)- (ii), (d)- (iv)

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