integration - Evaluating $ \int_ {1/2}^ {\infty} \frac {\Gamma (u ...
5 days ago · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, …
algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
Feb 21, 2025 · Well, the image equation is a different equation? One has $\frac1 {2024}$ on the right, and the other has $2024$ on the right?
integration - Evaluating $\sum_ {m=0}^\infty \sum_ {n=0}^\infty …
Nov 11, 2025 · I am evaluating the following integral: $$\\int_0^{1} \\left(\\tanh^{-1}(x) + \\tan^{-1}(x)\\right)^2 \\; dx$$ After using the Taylor series of the two functions, we ...
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 $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1/2x}}{x} $ without ...
Sep 11, 2024 · 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) …
Evaluating $ \\sum_{a \\in \\mathbb{N}}\\sum_{b \\in …
Sep 7, 2024 · The 1-D example is considerably easier, noticing that $\sum_ {n=1}^ {\lfloor x \rfloor} \frac {1} {n} = \ln (x) + \gamma + o (\frac {1} {x})$ The bounded function here is …
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 $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
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 $\int_0^1\left ( \frac {1} {\ln x} + \frac {1} {1-x} \right ...
Aug 8, 2024 · Is possible to evaluate \\begin{align*} \\int_0^1\\left[\\frac{1}{\\ln\\left(x\\right)} + \\frac{1}{1 - x}\\right]{\\rm d}x = \\gamma \\end{align*} using the fact ...
Evaluating $\lim_ {x\to 1}\frac {\left (\sum_ {k=1}^ {100}x^k\right ...
Aug 3, 2024 · $$\lim_ {x\to 1}\frac {\left (\sum_ {k=1}^ {100}x^k\right)-100} {x-1}$$ So I tried to do this problem with 2 methods. Method 1 gives me the correct answer whereas method 2 …