Question

$\sqrt{1+2(0.4)+3(0.4{)}^2+4(0.4{)}^3+\dots \dots \infty }$ has the value equal to

• A. $\frac{5}{3}$
• B. $\frac{5}{4}$
• C. 1
• D. $\frac{6}{5}$

Answer 1

Answer: (A)

$1+2x+3x^2+4x^3+\dots \dots \infty =\frac{1}{(1-x{)}^2}$
$\therefore \text{ square root is }\frac{1}{1-x}=\frac{1}{1-0.4}=\frac{1}{0.6}=\frac{5}{3}$