Recent questions tagged infinite-geometric-progression

An infinite geometric progression $a_{1},a_{2},a_{3},\dots\dots$ has the property that $a_n =3(a_{n+1}+a_{n+2}+\dots\dots)$ for every $n\geq 1$. If the sum $a_{1}+a_{2}+a...

Let $\text{S}$ denote the infinite sum $2+5x+9x^{2}+14x^{3}+20x^{4}+\ldots$where $\mid x \mid < 1$ and the coefficient of $x^{n-1}$ is $\dfrac{1}{2}n\left ( n+3 \right )...