First slide

Series of natural numbers

Question

If $1^{2} + 2^{2} + \dots + n^{2} = 1015$ , then value of $n$ is

Moderate

A

15
B

14
C

13
D

16

Solution

$\begin{array}{l} \frac{1}{6} n (n + 1) (2 n + 1) = 1015 \\ \Rightarrow (2 n) (2 n + 1) (2 n + 2) = (28) (29) (30) \\ \Rightarrow 2 n = 28 or n = 14 \end{array}$

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