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- algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b . . .
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- Evaluating $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
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 {x^ {14}+x^ {11}+x^5} { (x^6+x^3+1 . . .
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 $\cos (i)$ - Mathematics Stack Exchange
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- Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1 2x}}{x} $ without . . .
The following is a question from the Joint Entrance Examination (Main) from the 09 April 2024 evening shift: $$ \lim_ {x \to 0} \frac {e - (1 + 2x)^ {1 2x}} {x} $$ is equal to: (A) $0$ (B) $\frac {-2} {
- Evaluating $\int_ {-\infty}^ {\infty} \frac {x^6} { (1 + x^4)^2} dx$
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- 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 complex p
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