Sep 13, 2016 · Compute:$$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product. Is the product till infinity equal to $1$? If no, what is the answer?

Feb 19, 2016 · How does one prove the following limit? $$ \\lim_{n \\to \\infty} \\sqrt{1 + 2 \\sqrt{1 + 3 \\sqrt{1 + \\cdots \\sqrt{1 + (n - 1) \\sqrt{1 + n}}}}} = 3. $$

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I am trying to evaluate the integral $$\int \frac {1} {1+x^4} \mathrm dx.$$ The integrand $\frac {1} {1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I ...

How would you evaluate the following series? $$\\lim_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n^2+k^2} $$ Thanks.

Mar 24, 2017 · A lot of questions say "use polar coordinates" to calculate limits when they approach $0$. But is using polar coordinates the best way to evaluate limits, moreover, prove that they exist? Do they

Dec 7, 2018 · I see now how I can go about evaluating the limit itself although I still find the concept a little bit vague, as in considering a specific order for the expansion and then applying it for all the …

Apr 23, 2017 · Evaluate the contour integral $\int_C\frac {z+1} {z^2-2z}dz$ using Cauchy's residue theorem, where $C$ is the circle $|z|=3$. I see that the function has 2 ...