શ્રેણીનો સરવાળો શોધો: $\log_e \frac{4}{5} + \frac{1}{4} - \frac{1}{2} \left( \frac{1}{4} \right)^2 + \frac{1}{3} \left( \frac{1}{4} \right)^3 - \dots$

  • A
    $2 \log_e \frac{4}{5}$
  • B
    $\log_e \frac{5}{4}$
  • C
    $1$
  • D
    $0$

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જો $4\left[ {{x^2} + \frac{{{x^6}}}{3} + \frac{{{x^{10}}}}{5} + \dots} \right] = {y^2} + \frac{{{y^4}}}{2} + \frac{{{y^6}}}{3} + \dots$ હોય,તો

$\frac{2}{1} \cdot \frac{1}{3} + \frac{3}{2} \cdot \frac{1}{9} + \frac{4}{3} \cdot \frac{1}{27} + \frac{5}{4} \cdot \frac{1}{81} + \dots \infty = $

શ્રેણી $\log_{4} 2 - \log_{8} 2 + \log_{16} 2 - \dots$ નો સરવાળો કેટલો થાય?

$\cosh^{-1} 2 = $

જો $\tanh ^{-1} x = a \log \left(\frac{1+x}{1-x}\right)$, $|x| < 1$ હોય, તો $a$ ની કિંમત શોધો.

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