series

Let Pk represent the perimeter of a square with sides of length k. The value of the expression P₁ + P₂ + P₃ + ⋯ + P₁₀ is

Consider the two series, $S_A$ and $S_B$, where $S_A = \sum_{n=1}^{\infty} \frac{n^2}{2^n}$ $S_B = 1 + \frac{1}{2} + \frac{1}{8} + \frac{1}{16} + \frac{1}{64} + \frac{1}{128} + \fr...

Consider the following series: (i) $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ (ii) $\sum_{n=1}^{\infty} \frac{1}{n(n+1)}$ (iii) $\sum_{n=1}^{\infty} \frac{1}{n!}$ Choose the correct...

The sum of n terms of the series 4 + 44 + 444 +.... is