Special series Calculator

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Calculates the sum of the selected special series.

\(\normalsize
(1)\ {\large\displaystyle \sum_{\small k=1}^{\small n}}k ={\large\frac{n(n+1)}{2}}\\
(2)\ {\large\displaystyle \sum_{\small k=1}^{\small n}}k^2 ={\large\frac{n(n+1)(2n+1)}{6}}\\
(3)\ {\large\displaystyle \sum_{\small k=1}^{\small n}}k^3 ={\large\frac{n^2(n+1)^2}{4}}\\
(4)\ {\large\displaystyle \sum_{\small k=1}^{\small n}}k(k+1) ={\large\frac{n(n+1)(n+2)}{3}}\\
(5)\ {\large\displaystyle \sum_{\small k=1}^{\small n}\frac{1}{k(k+1)}} ={\large\frac{n}{n+1}}\\
(6)\ {\large\displaystyle \sum_{\small k=1}^{\small n}}k(k+1)(k+2) ={\large\frac{n(n+1)(n+2)(n+3)}{4}}\\
(7)\ {\large\displaystyle \sum_{\small k=1}^{\small n}\frac{1}{k(k+1)(k+2)}} ={\large\frac{n(n+3)}{4(n+1)(n+2)}}\\
\)

Special series Calculator

Calculates the sum of the selected special series.

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Special series Calculator

Calculates the sum of the selected special series.

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History

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