Question

The value of $1+\frac{1}{4\times 3}+\frac{1}{4\times 3^2}+\frac{1}{4\times 3^3}+\frac{1}{4\times 3^4}$ is?

• A. $\frac{121}{108}$
• B. $\frac{3}{2}$
• C. $\frac{31}{2}$
• D. $\frac{91}{81}$

Answer 1

The correct option is D $\frac{91}{81}$

$1+\frac{1}{4\times 3}+\frac{1}{4\times 3^2}+\frac{1}{4\times 3^3}+\frac{1}{4\times 3^4}$

$=1+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}$

$=\frac{324+27+9+3+1}{324}$

$=\frac{364}{324}$

$=\frac{91}{81}$

Hence, the answer is $\frac{91}{81}.$