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What is the sum of the series 152 + 162 + 172 + ..... + 302 equal to? |
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Answer» 152 + 162 + 172 + ..... + 302 = (12 + 22 + 32 + .... + 302) – (12 + 22 + 32 + ..... + 142) = \(\displaystyle\sum_{k=1}^{30} k^2\) - \(\displaystyle\sum_{k=1}^{14} k^2\) = \(\frac{1}{6}\) x 30 x 31 x (2 x 30 + 1) - \(\frac{1}{6}\)x 14 x 15 x (2 x 14 + 1) \(\bigg(\because\,\displaystyle\sum_{k=1}^{n} k^2\, =\frac{1}{6}\times{n}(n+1)(2n+1)\bigg)\) = \(\frac{30\times31\times61}{6}\) - \(\frac{14\times15\times29}{6}\) = 9455 – 1015 = 8440. |
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