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- Evaluating $\\int_0^1 (1-x^2)^n dx$ - Mathematics Stack Exchange
Evaluating ∫1 0 (1 − x2)ndx ∫ 0 1 (1 x 2) n d x [duplicate] Ask Question Asked 4 years, 4 months ago Modified 4 years, 4 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
- algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b . . .
When I tried to solve this problem, I found a solution (official) video on YouTube That is a = −b, c = 2024 a = b, c = 2024 and the correct answer is 1 20242025 1 2024 2025 Is there an alternative solution but not using (a + b)(a + c)(b + c) + abc = (a + b + c)(ab + ac + bc) (a + b) (a + c) (b + c) + a b c = (a + b + c) (a b + a c + b c) ?
- Evaluating $\\int_0^1 \\frac{x\\arctan(x)}{1-x^2} \\log^2 \\left . . .
has long been famous in this place, and a relevant link is this one Evaluating ∫1 −1 arctanx 1+x ln(1+x2 2)dx ∫ 1 1 arctan x 1 + x ln (1 + x 2 2) d x, where you can find solutions using real and complex methods
- 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
- Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1 2x}}{x} $ without . . .
Evaluating limx→0 e−(1+2x)1 2x x lim x → 0 e (1 + 2 x) 1 2 x x without using any expansion series [closed] Ask Question Asked 10 months ago Modified 10 months ago
- Evaluating $\\lim\\limits_{R\\to +∞}\\iint_{x^2+y^2\\leq R^2}\\left . . .
I wonder whether you would agree that the second line above is easier to read than the first Note (1) the use of \left and \right, which makes the parentheses assume appropriate sizes, (2) the use of \limits, which affects the position of the bounds of integration, and (3) small spaces separating dx d x and dy d y from what precedes and follows them
- sequences and series - Evaluating $\sum_ {n=1}^ {\infty} 1 \phi (n)^2 . . .
Wolfram Alpha gives $$\sum_ {n=1}^ {10000} 1 \phi (n)^2\approx 3 3901989747265619591157$$ and a graph of partial sums indicates fairly clearly this converges: It's well-known that the sum of the inv
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