Question

find
5²+6²+7²+.......30²

Answer 1

     

$\Rightarrow\ 5^2+6^2+7^2+...+30^2 \\ \\ \Rightarrow\ 1^2+2^2+3^2+...+30^2-1^2-2^2-3^2-4^2 \\ \\ \Rightarrow\ (1^2+2^2+3^2+...+30^2)-(1^2+2^2+3^2+4^2) \\ \\ \Rightarrow\ (\frac{30 \times 31 \times 61}{6})-(\frac{4 \times 5 \times 9}{6}) \\ \\ \Rightarrow\ (5 \times 31 \times 61)-(2 \times 5 \times 3) \\ \\ \Rightarrow\ 9455-30 \\ \\ \Rightarrow\ \textit{9425}$

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