Let $n$ be the smallest positive integer such that $1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{n} \geq 4$. Which one of the following statements is true?

If $\sum\limits_{r=1}^\infty \frac{1}{(2r-1)^2} = \frac{\pi^2}{8}$,then $\sum\limits_{r=1}^\infty \frac{1}{r^2} = \dots$

What is the sum of $n$ terms of the series $2 + 5 + 14 + 41 + \dots$?

If $n$ is odd or even,the sum of $n$ terms of the series $1 - 2 + 3 - 4 + 5 - 6 + \dots$ is given by:

Let $b_1, b_2, \dots, b_n$ be a geometric sequence such that $b_1 + b_2 = 1$ and $\sum\limits_{k = 1}^\infty b_k = 2$. Given that $b_2 < 0$,then the value of $b_1$ is:

Let $\alpha = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots \infty$ and $\beta = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots \infty$. Then the value of $(0.2)^{\log_{\sqrt{5}}(\alpha)} + (0.04)^{\log_{5}(\beta)}$ is equal to: