If 1-1-3-1-5-1-7- -4 then 1-1-3-1-5-7-1-9-11- - - -

The correct option is D π/4 = (1 1/3) + (1/5 nbsp;1/7) + (1/9 nbsp;1/11) + ......... ⇒ nbsp;2/1.3 + nbsp;2/5.7 + nbsp;2/9.11 + ........ = nb ...

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Algebra of Complex Numbers

If 1-1/3+1/5-...

Question

If 1 - $\frac{1}{3}$ + $\frac{1}{5}$ - $\frac{1}{7}$ +....... = $\frac{π}{4}$ then $\frac{1}{1.3}$ + $\frac{1}{5.7}$ + $\frac{1}{9.11}$ + ...... =

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1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \frac{1}{11} + . . . = \frac{π}{4}

\frac{1}{1.3} + \frac{1}{5.7} + \frac{1}{9.11} + . . . =

\frac{1}{1.3} + \frac{1}{5.7} + \frac{1}{9.11} + . . . t o \infty

1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} + \dots = \frac{π}{4},

\frac{1}{1 \times 3} + \frac{1}{5 \times 7} + \frac{1}{9 \times 11} + \dots

${lim}_{n \to \infty} [\frac{1}{1.3} + \frac{1}{3.5} + \frac{1}{5.7} \dots \frac{1}{(2 n + 1) (2 n + 3)}]$ is equa to

\frac{n (4 n^{2} + 6 n - 1)}{3}

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