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?
Evaluating $\\lim_{x\\to1}\\frac{m}{1-x^m} -\\frac{n}{1+x^n}$, for ...
Nov 11, 2025 · $$\\lim_{x\\to1}\\frac{m}{1-x^m} -\\frac{n}{1+x^n} \\;\\;\\;\\;\\;\\; m,n\\in \\mathbb{N}$$ My teacher had given the class this sum as homework. He gave us a hint ...
calculus - Evaluating $\int {\frac {x^ {14}+x^ {11}+x^5}
Jul 2, 2025 · The following question is taken from JEE practice set. Evaluate $\\displaystyle\\int{\\frac{x^{14}+x^{11}+x^5}{\\left(x^6+x^3+1\\right)^3}} \\, \\mathrm dx$. My ...
Evaluating a Complex Integral involving Bessel Function
Jan 12, 2025 · Evaluating a Complex Integral involving Bessel Function Ask Question Asked 10 months ago Modified 10 months ago
Evaluating $\cos (i)$ - Mathematics Stack Exchange
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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 $\lim\limits_ {n\to\infty} e^ {-n} \sum\limits_ {k=0}^ {n ...
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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 integrals with sigma notation - Mathematics Stack …
Evaluating integrals with sigma notation Ask Question Asked 13 years, 7 months ago Modified 8 years, 6 months ago
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.