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

MCQ

If ∑ n = 210, then ∑ n2 =

Options

  •  2870

  • 2160

  • 2970

  • none of these

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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,

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

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

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

\[ \Rightarrow \left( 70 \right) \times \left( 41 \right)\]

\[ \Rightarrow 2870\]

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APPEARS IN

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