New posts in Sequences And Series

Showing the sequence $\sqrt{2}, \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}, \dots$ tends to $2$ using the Epsilon-Neighbourhood definition

How to calculate $ \int_0^{\pi/2}\log(1+\sin(x))\log(\cos(x)) \,dx $?

Why does this pattern work: $1 \cdot{1} = 1, 11 \cdot{11} = 121, 111 \cdot{111} = 12321\ldots$

Why should we care about sequence in real analysis?

$\frac 21 \times \frac 43 \times \frac 65 \times \frac 87 \times \cdots \times \frac{9998}{9997} \times \frac {10000}{9999} > 115$

$\frac{2}{3} \cdot \frac{5}{6} \cdot \frac{8}{9} \cdot ... \cdot \frac{995}{996} \cdot \frac{998}{999}$ and $0.1$ which is bigger?

Follow-up Question about Cesaro mean proof

Does ``Converge to'' and ``Strict Equality'' Always Mean the Same Thing? If Not, is This a Paradox?

How to find a real sequence $x_n$ such that $n x_n \to 0$ as $n \to \infty$ and $\sum_{n=1}^{\infty} x_n$ diverges?

Analyse convergence of: $\displaystyle \sum^{\infty}_{n=3} \left (\sqrt[3]{n^3 + 2} - \sqrt{n^2 + 7}\right)$