Series - Problem 5

Algebra Level 4

$1 + \frac{3}{4} + \frac{3\times 5}{4\times 8} + \frac{3\times5\times7}{4\times8\times12} + \ldots = ?$

\sqrt[3]{32}

\sqrt{5}

\sqrt{8}

\sqrt{\frac{7}{2}}

1 solution

Fahim Shahriar Shakkhor
Sep 25, 2014

Let, $(1-x)^{-n} = 1 + nx + \dfrac{n(n+1)}{2}x^2+......$

Now,

$nx = \frac{3}{4} \\ \dfrac{n(n+1)}{2}x^2 = \dfrac{3\times5}{4\times8} \Longrightarrow (n+1)x=\frac{5}{4}$

Here,

$x=\dfrac{1}{2}$ , $n=\dfrac{3}{2}$

Putting the values,

$1 + nx + \dfrac{n(n+1)}{2}x^2+...... = (1-\dfrac{1}{2})^{-\frac{3}{2}} = 2^{\frac{3}{2}} = \sqrt {8}$

Hi, I would just like to ask why the first statement in the solution is true.

Neil Chua Goy - 6 years, 6 months ago

one of the options was illegible........ that can be quite confusing bro!!

Mayank Holmes - 6 years, 8 months ago

How to even start ??

Vishal Yadav - 4 years, 2 months ago