The value of $\mathop \sum \limits_{n = 0}^\infty {\left( {\frac{{2i}}{3}} \right)^n}$ is

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

The value of

\sum \limits_{n = 0}^\infty {\left( {\frac{{2i}}{3}} \right)^n}

View answer and explanation

Correct option: A

\frac{{9 + 6i}}{{13}}

Option A ((9 + 6i)/13) is correct because the given expression is an infinite geometric series, and its sum can be calculated using the formula for the sum of an infinite geometric series.

More Questions from COMPLEX NUMBERS

Practice All Chapter MCQs →

The number of non-zero integer solutions of the equation

{\left| {1 - i} \right|^x} = {2^x}

is If

|z|=1

and

z \neq \pm 1

, then for any complex number

z, \frac{z}{1-z^2}

Let

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

, then

\left|\sum\limits_{r=1}^n z_r\right|

is less than The roots of the cubic equation

(z+a b)^3=a^3

, where

a \neq 0

represents the vertices of a triangle. If

\alpha, \beta

and

\gamma

are the roots, then find the value of

|\alpha-\beta|

. Number of solutions of the equation

{z^2} + {\left| z \right|^2} = 0,

where

z \in C

is If

2x = - 1 + \sqrt 3 i

, then the value of

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}

is equal to