$8,88,888,8888 \ldots$ શ્રેણીનાં પ્રથમ $n$ પદોનો સરવાળો શોધો. 

The given sequence is $8,88,888,8888 \ldots$

This sequence is not a $G.P.$ However, it can be changed to $G.P.$ by writing the terms as

$S_{n}=8+88+888+8888+\ldots \ldots$ to $n$ terms

$=\frac{8}{9}[9+99+999+9999+\ldots \ldots . . $ to $ n $ terms $]$

$=\frac{8}{9}\left[\left(10+10^{2}+\ldots \ldots . n \text { terms }\right)-(1+1+1+\ldots . . n \text { terms })\right]$

$=\frac{8}{9}\left[\frac{10\left(10^{n}-1\right)}{10-1}-n\right]$

$=\frac{8}{9}\left[\frac{10\left(10^{n}-1\right)}{9}-n\right]$

$=\frac{80}{81}\left(10^{n}-1\right)-\frac{8}{9} n$