Matematik

$\sum_{n=1}^{\infty}(\frac{3n}{3n-1})^{n!}$

Regarding this sum $\sum_{n=1}^{\infty}(\frac{3n}{3n-1})^{n!}$ I need to tell if it converges or diverges. Here is my attempt: $\sum_{n=1}^{\infty}(\frac{3n}{3n-1})^{n!}...

Find $\int_0^1 \dfrac{f(x)}{\sqrt{1+x^2}}$

Let $f(x)$ be continuous on $[0;1]$, with $f(0) = 0; f(1) = 1$ and $$\int_0^1 [f'(x)]^2 \sqrt{1+x^2} \,dx = \dfrac{1}{\ln\left(1+\sqrt{2}\right)}$$...

Trigonometric functions question

What's $\tan^{-1}$$(1+i)$ how can I solve it if someone help us?

Relating integrals to a square

The following problem is a problem in my linear algebra book. (a) Compute the following integrals (you can use a calculator) and state...

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