Special series Calculator

Calculates the sum of the selected special series.

 special series Σ k k^2 k^3 k(k+1) 1/k(k+1) k(k+1)(k+2) 1/k(k+1)(k+2) number of terms n n＝1,2,3... 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt sum Sn
 $\normal (1)\ {\large\sum_{\small k=1}^{\small n}}k ={\large\frac{n(n+1)}{2}}\\(2)\ {\large\sum_{\small k=1}^{\small n}}k^2 ={\large\frac{n(n+1)(2n+1)}{6}}\\(3)\ {\large\sum_{\small k=1}^{\small n}}k^3 ={\large\frac{n^2(n+1)^2}{4}}\\(4)\ {\large\sum_{\small k=1}^{\small n}}k(k+1) ={\large\frac{n(n+1)(n+2)}{3}}\\(5)\ {\large\sum_{\small k=1}^{\small n}\frac{1}{k(k+1)}} ={\large\frac{n}{n+1}}\\(6)\ {\large\sum_{\small k=1}^{\small n}}k(k+1)(k+2) ={\large\frac{n(n+1)(n+2)(n+3)}{4}}\\(7)\ {\large\sum_{\small k=1}^{\small n}\frac{1}{k(k+1)(k+2)}} ={\large\frac{n(n+3)}{4(n+1)(n+2)}}\\$

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