Question

Summation of this series ${1\over 2}\left[1+{1 \over 3}\left({1 \over 4}\right)^2+ {1 \over 5}\left({1 \over 4}\right)^4+\cdots\right]$

score 177 · Answer 1 · 2026-04-17 11:14:38

Summation of this series ${1\over 2}\left[1+{1 \over 3}\left({1 \over 4}\right)^2+ {1 \over 5}\left({1 \over 4}\right)^4+\cdots\right]$

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List Question

Summation of this series ${1\over 2}\left[1+{1 \over 3}\left({1 \over 4}\right)^2+ {1 \over 5}\left({1 \over 4}\right)^4+\cdots\right]$

Proving quadratic convergence implies superlinear convergence

Sequence can converge linearly with one norm but not another, and superlinear convergence does not depend on norm

How can I prove this sequence convergent?

about limit of exponential function

Proving $\frac{a_n}{n^2}$ is bounded above

Taylor series of $\ln(1+(1/x))$

Prove that $\{f_n\}^{\infty}_{n=1}$ is equicontinuous $K$ if $\{f_n\}^{\infty}_{n=1}$ is uniformly convergent on $K$

Finding a missing number of a sequence based on the average and median

How can I represent following series as a formula?

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Finding a closed form for $\sum_{n = 1}^{\infty} \frac{1}{(1 + x^2)^{n}}$

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