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Question Number 72694 by MJS last updated on 31/Oct/19

$$\mathrm{convergent}\mathrm{or}\mathrm{divergent}?$$$$S=\frac{2}{1}-\frac{1}{1}+\frac{2}{3}-\frac{1}{3}+\frac{2}{5}-\frac{1}{5}+\frac{2}{7}-\frac{1}{7}...$$

Commented by mathmax by abdo last updated on 31/Oct/19

$$S=\sum _{n=0}^{\mathrm{\infty }}\frac{2}{2n+1}-\sum _{n=0}^{\mathrm{\infty }}\frac{1}{2n+1}\Rightarrow S=\sum _{n=0}^{\mathrm{\infty }}(\frac{2}{2n+1}-\frac{1}{n+1})$$$$=\sum _{n=0}^{\mathrm{\infty }}\frac{1}{2n+1}andthisseriediverges.$$

Commented by MJS last updated on 31/Oct/19

$$\mathrm{thank}\mathrm{you}$$

Commented by mathmax by abdo last updated on 31/Oct/19

$$youarewelcomesirmjs.$$

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