Find coefficient of $x^n$ in $(1+x+2x^2+3x^3+.....+nx^n)^2$

Evaluating $\int_0^{1/2} \log(1-x) \log(1-2x) \ dx$.

Prove that $\sum\limits_{cyc}\frac{a}{a+b}\geq1+\frac{3\sqrt[3]{a^2b^2c^2}}{2(ab+ac+bc)}$

Why is modular arithmetic defined as a "similarity" and not an operation?

Show that :$\int_{0}^{1}(1-x^2)^ndx={(2n)!!\over (2n+1)!!}$

Showing that $f(x) = x^3$ is injective?

Volume of sphere-cube intersection

Can we really intersect circles?

Show that the Area of image = Area of object $\cdot |\det(T)|$? Where $T$ is a linear transformation from $R^2 \rightarrow R^2$

If $a+b+c = 6$ and $a$, $b$, $c$ are nonnegative then $a^2+b^2+c^2 \geq 12$

Is there an existing theory of Pythagorean triples for numbers of the form $p+q\sqrt r$ rather than integers?

How to "coordinate bash" a geometry problem?

Find all the prime factors of $1000027$

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