Tag: sequence, progression and series

The value of $3 - 1 + \frac{1}{3} - \frac{1}{9} +  \ldots $ is equal to

Let $P = 3^{1/3} . 3^{2/9} . 3^{3/27} ...\infty$, then $P^{1/3}$ is equal to

The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$ will be

The value of $9^{1/3}\times 9^{1/9} \times 9^{1/27} \times .....\infty$ is

The value of $9^\cfrac{1}{3}.9^\cfrac{1}{9}.9^\cfrac{1}{27}...........$ upto $\infty$, is

If $x=1+a+{ a }^{ 2 }+{ a }^{ 3 }+....$ to $\infty \left( \left| a \right| <1 \right) $ and 
$y=1+b+{ b }^{ 2 }+{ b }^{ 3 }+...$ to $\infty \left( \left| b \right| <1 \right) $ then
$1+ab+{ a }^{ 2 }{ b }^{ 2 }+{ a }^{ 3 }{ b }^{ 3 }+...$ to $\infty =\cfrac { xy }{ x+y-1 } $

The sum to infinity of the series $1 + \dfrac{2}{3} + \dfrac{6}{{{3^2}}} + \dfrac{{10}}{{{3^3}}} + \dfrac{{14}}{{{3^4}}} + ......,is$

If $x = 1\, + a + {a^2} + ......\infty $, $y = 1\, + b + {b^2}\,\, + ......\infty $ where $\left| a \right| < 1$ and $\left| b \right| < 1$, then $\left( {1 + ab + {a^2}{b^2} + ........\infty } \right) = ?$

Value of $y = {\left( {0.64} \right)^{{{\log } _{0.25}}\left( {\cfrac{1}{3} + \cfrac{1}{{{3^2}}} + \cfrac{1}{{{3^3}}}....upto   \infty } \right)}}$ is :

If $y=x-x^2+x^3-x^4+....\infty$, then value of x will be?