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1d
comment What kinds of things are infinite series useful for?
One should look at how useful are these series for practical computation.
1d
comment What kinds of things are infinite series useful for?
I think by series being useful you mean power series, as they are the simplest things to work with. There are many types of series that are interesting but not useful for practical use, e.g. then common Arctan series that gives the value for $\pi$.
1d
comment Proof $(\log(n))^{\log(\log(n))} = O(n)$
does $\log(n)^{\log(\log(n))} $ mean $\log(n^{\log(\log(n))}) $ or $(\log n)^{\log(\log(n))} $?
1d
comment Proof $(\log(n))^{\log(\log(n))} = O(n)$
This notation is a bit ambiguous. What does $\log^{\log(\log(n))}$ mean?
1d
revised Prove $2\cos^2(x)=1+\cos(2x)$
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1d
comment Divergent products.
@GEdgar : lets be nice :)
2d
revised Integral $ \int \frac{1}{x^{1+a} (1-x)^{1-a}} dx~,~a \gt 0$
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2d
comment sequences and convergence
1 question per post please also show your work.
Jan
28
comment Solve $\int_0^\infty \frac{\ln x}{x^2+4} \,\mathrm{d}x$
Integrals are evaluated not solved. "Solve" for what?
Jan
28
revised Integral $\int \frac{1}{(4x^2-8x+3)^{1/2}}$
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Jan
28
revised Solve $\int_0^\infty \frac{\ln x}{x^2+4} \,\mathrm{d}x$
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Jan
28
revised convergence of $\sum_{n=1}^\infty\frac{1}{n} [1+\frac{1}{\sqrt{2}}+…+\frac{1}{\sqrt{n}}]$
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Jan
28
comment convergence of $\sum_{n=1}^\infty\frac{1}{n} [1+\frac{1}{\sqrt{2}}+…+\frac{1}{\sqrt{n}}]$
compare with $\frac{1}{n \ln n}$
Jan
28
revised How to get to $5^3 \geq n^3$ in the proof by contradiction?
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Jan
28
revised Sum $(1-x)^n$ $\sum_{r=1}^n$ $r$ $n\choose r$ $(\frac{x}{1-x})^r$
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Jan
28
revised Integral $\int\frac{(\ln x)^{10}}{x}\,dx$
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Jan
28
revised Integral $\int_0^\infty e^{-x/2}x\log(1+kx^2)\,dx$
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Jan
28
revised Integral $\int_{0}^{\infty}\frac1{\sqrt[\alpha]{1+x^\beta}}dx$
added 1 character in body
Jan
28
comment Integral $\int_{0}^{\infty}\frac1{\sqrt[\alpha]{1+x^\beta}}dx$
@Travis : what are the most possible general values that they can assume? Initially them being real I guess but would complex or even matrix values be possible?
Jan
28
asked Integral $\int_{0}^{\infty}\frac1{\sqrt[\alpha]{1+x^\beta}}dx$