# If ∑ N = 210, Then ∑ N2 = - Mathematics

MCQ

If ∑ n = 210, then ∑ n2 =

#### Options

•  2870

• 2160

• 2970

• none of these

#### Solution

2870

Given:
∑n = 210

$\Rightarrow n\left( \frac{n + 1}{2} \right) = 210$

$\Rightarrow n^2 + n - 420 = 0$

$\Rightarrow \left( n - 20 \right)\left( n + 21 \right) = 0$

$\Rightarrow n = 20 \left( \because n > 0 \right)$

Now,

$\sum^{}_{} n^2 = \frac{n\left( n + 1 \right)\left( 2n + 1 \right)}{6}$

$\Rightarrow \frac{n(n + 1)}{2} \times \frac{(2n + 1)}{3}$

$\Rightarrow \left( 210 \right) \times \left( \frac{41}{3} \right)$

$\Rightarrow \left( 70 \right) \times \left( 41 \right)$

$\Rightarrow 2870$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 21 Some special series
Q 4 | Page 19