Question

Find S15 of the series : 2 + 5 + 10 + 17 + 26 + .....​

Answer 1

Step-by-step explanation:

Given:2 + 5 + 10 + 17 + 26 + .....

To find:S15

Solution:

To find the sum of first 15 terms of given series,first check the pattern of series

$2 + 5 + 10 + 17 + 26 + ... \\ \\ ( {1)}^{2} + 1 + ( {2)}^{2} + 1 + ( {3)}^{2} + 1 + ( {4})^{2} + 1 + ( {5)}^{2} + 1 + ...$

So,

general term of this series is

$T_n = {n}^{2} + 1$

To find the sum of n terms of the series

$S_n = \Sigma(T_n) \\ \\ S_n = \Sigma( {n}^{2} + 1)$

Sum of 15 terms

$S_{n} = _{n = 1} ^{15} \Sigma( {n}^{2} + 1) \\ \\ S_n =_{n = 1} ^{15} \Sigma {n}^{2} + _{n = 1} ^{15}\Sigma \: 1 \\ \\ S_{n}= \frac{n(n + 1)(2n + 1)}{6} + n \\ \\ S_{15}= \frac{15(15 + 1)(15 \times 2 + 1)}{6} + 15 \\ \\ S_{15}= \frac{15 \times 16 \times 31}{6} + 15 \\ \\ S_{15}= 5 \times 8 \times 31 + 15 \\ \\ S_{15}= 40 \times 31 + 15 \\ \\ S_{15}= 1240 + 15 \\ \\ S_{15} = 1255$

Sum of 15 terms of the series is 1255.

Hope it helps you.

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