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Finding sums for an infinite class of convergent series. (English)
Int. J. Math. Educ. Sci. Technol. 47, No. 4, 649-651 (2016).
Summary: We use Leibniz’s rule and the cotangent function to evaluate the following infinite series $\sum_{k=1}^{\infty}\frac{1}{k^2}$, $\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{(2k-1)^3}$, $\sum_{k=1}^{\infty}\frac{1}{k^4}$, $\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{(2k-1)^5}$,\dots .
Classification: I30 F60