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  2. complex analysis - Contour integral for $x^3/(e^x-1)$? - Mathematics ...

    What contour and integrand do we use to evaluate $$ \\int_0^\\infty \\frac{x^3}{e^x-1} dx $$ Or is this going to need some other …

  3. exponential function - Prove by induction that (5^ (n))-1 is divisible ...

    Prove by induction that $5^n-1$ is divisible by $4$ for all natural numbers $n$. I got $P(k+1)=5^{k+1}-1$ but I don't where to go now.

  4. 1-1+1-1+1-1+1... 这个无穷数列的值是什么?如何证明? - 知乎

    知乎,中文互联网高质量的问答社区和创作者聚集的原创内容平台,于 2011 年 1 月正式上线,以「让人们更好的分享知识、经验和见 …

  5. 如何证明数学等式 1 + 1 = 2 的成立? - 知乎

    我:因为1+1=2。 A君:你这是循环论证,诡辩,没有意义的。 我:1+1=2是公理,你质疑它,所以你的问题也是没有意义的。 A君: …

  6. Inverse of the sum of matrices - Mathematics Stack Exchange

    May 24, 2015 · The technique is useful in computation, because if the values in A and B can be very different in size then calculating …

  7. Simplify K!/ (K+1)! - Mathematics Stack Exchange

    Mar 9, 2016 · Pretend K=3 That means (K+1)= 4 This means you'd be dividing 3*2*1 by 4*3*2*1. Consider how you'd cancel out …

  8. Using the definition of a limit to prove 1/n converges to zero.

    Aug 6, 2015 · What this says is that eventually, every term of the sequence 1 n 1 n $\frac{1}{n}$ is close to 0 0 $0$, no matter how …

  9. Is the square root of -1 rational? - Mathematics Stack Exchange

    $\sqrt{-1}=i$ is an imaginary number, not lying anywhere on the real number line. Therefore as others have said, it is neither rational …

  10. combinatorics - Sum of $k {n \choose k}$ is $n2^{n-1}$ - Mathematics ...

    Factor out the n n $n$ using given identity and adjust the remaining sum so that you can use the known sum of binomial coefficients.

  11. 1 and 2 norm inequality - Mathematics Stack Exchange

    While looking over my notes, my lecturer stated the following inequality;