Question

If sigma n=55, then sigma n square is equal to :
(A) 3025
(B) 506
(C)385
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Answer 1

(C)385

The value of $\sum n^2$ is 385.

Explanation:

We know that the the sum of 1+2+3+4+......+n = $\sum n = \dfrac{n(n+1)}{2}$

As per given , $\dfrac{n(n+1)}{2}=55$

$\\\\ n^2+n= 110\\\\ n^2+n-110=0\\\\ n^2+11n-10n-110=0\\\\ (n+11)(n-10)=0\\\\ n=-11\ or\ n=10$

Here , n is a natural number so we take , n= 10

Now , the sum of 1²+2²+3²+4²+......+n² =$\sum n^2=\dfrac{n(n+1)(2n+1)}{6}$

At n= 10 , we have

$\sum n^2=\dfrac{10(10+1)(2(10)+1)}{6}=385$

Hence, the value of $\sum n^2$ is 385.

Thus , the correct answer is (C)385

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