Question

The sum of the series $5.05+1.212+0.29088+...........\infty$ is

• A. $6.93378$
• B. $6.87342$
• C. $6.74384$
• D. $6.64474$

Answer 1

The correct option is D

$6.64474$

Explanation for correct option

Given: $5.05+1.212+0.29088+...........\infty$

Let $r$ be the common ratio

$$\begin{gathered} r=\frac{1.212}{5.05} \\ \Rightarrow r=0.24 \end{gathered}$$

$5.05+1.212+0.29088+...........$ is a geometric progression with first term $a=5.05$ and common ratio $r=0.24$

sum of geometric progression$=a\left[\frac{r^{n-1}}{r-1}\right]$

sum of $5.05+1.212+0.29088+...........\infty$$=\frac{5.05}{1-0.24}$

$5.05+1.212+0.29088+...........\infty$$=\frac{5.05}{0.76}$

$5.05+1.212+0.29088+...........\infty$$=6.644736842105263$

$5.05+1.212+0.29088+...........\infty$$\approx 6.64474$

Hence,$\mathrm{Option}\left(\mathrm{D}\right)$ is correct.