Evaluating the nested radical $ \sqrt {1 + 2 \sqrt {1 + 3 \sqrt {1 ...
Feb 19, 2016 · How does one prove the following limit? $$ \\lim_{n \\to \\infty} \\sqrt{1 + 2 \\sqrt{1 + 3 \\sqrt{1 + \\cdots \\sqrt{1 + (n - 1) \\sqrt{1 + n}}}}} = 3. $$
Evaluating $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
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?
calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
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 ...
Evaluating $\cos (i)$ - Mathematics Stack Exchange
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Evaluating $\\int_0^{\\infty}\\frac{\\ln(x^2+1)}{x^2+1}dx$
How would I go about evaluating this integral? $$\int_0^ {\infty}\frac {\ln (x^2+1)} {x^2+1}dx.$$ What I've tried so far: I tried a semicircular integral in the positive imaginary part of the …
Evaluating a Complex Integral involving Bessel Function
Jan 12, 2025 · Evaluating a Complex Integral involving Bessel Function Ask Question Asked 9 months ago Modified 9 months ago
Evaluating the limit using Taylor Series - Mathematics Stack …
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 …
integration - Evaluating $\int_0^ {\pi/2} \frac {\sqrt [3] {\tan x ...
Feb 26, 2023 · I would like to solve the first problem of the 2023 MIT Integration Bee Finals, which is the following integral : $$\int_0^ {\pi/2} \frac {\sqrt [3] {\tan x}} { (\cos x + \sin x)^2}dx$$ I tried …
Evaluating $ \lim\limits_ {n\to\infty} \sum_ {k=1}^ {n^2} \frac {n} {n ...
How would you evaluate the following series? $$\\lim_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n^2+k^2} $$ Thanks.
Evaluating $\lim\limits_ {n\to\infty} e^ {-n} \sum\limits_ {k=0}^ {n ...
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