If $1 + r + r^2 + \dots + r^n = (1 + r) (1 + r^2) (1 + r^4) (1 + r^8)$,then what is the value of $n$?

Consider an infinite geometric series with first term $a$ and common ratio $r$. If its sum is $4$ and the second term is $3/4$,find the values of $a$ and $r$.

If $p, q, r$ are in a geometric progression and $a, b, c$ are in another geometric progression,then $cp, bq, ar$ are in...

If $a, b, c$ and $d$ are in $G.P.$,show that:
$(a^{2}+b^{2}+c^{2})(b^{2}+c^{2}+d^{2})=(ab+bc+cd)^{2}$

In a $G.P.$, if the product of the first three terms is $27$ and the set of all possible values for the sum of its first three terms is $\mathbb{R} - (a, b)$, then $a^{2} + b^{2}$ is equal to . . . . . . .

The value of ${4^{1/3}} \cdot {4^{1/9}} \cdot {4^{1/27}} \cdots \infty$ is