Question

$\underset{x\to \infty }{lim}\{1+\frac{1}{5}+\frac{1}{5^2}+.........+\frac{1}{5^n}\}=$

• A. $1$
• B. $0$
• C. $\frac{4}{5}$
• D. $\frac{5}{4}$

Answer 1

Answer: (D)

$\frac{5}{4}$

$\underset{x\to \infty }{lim}\{1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^x}\}$

$=\underset{x\to \infty }{lim}\frac{1(1-{\left(\frac{1}{5}\right)}^{x+1})}{1-\frac{1}{5}}$

$=\underset{x\to \infty }{lim}\frac{5}{4}(1-\frac{1}{5^{x+1}})$

$=\frac{5}{4}(1-\frac{1}{5^{\infty }})=\frac{5}{4}(1-0)=\frac{5}{4}$