Find the sum to indicated number of terms in each of the geometric progressions in $\left.x^{3}, x^{5}, x^{7}, \ldots n \text { terms (if } x \neq\pm 1\right)$
Find the sum to indicated number of terms in each of the geometric progressions in $\left.x^{3}, x^{5}, x^{7}, \ldots n \text { terms (if } x \neq\pm 1\right)$
The given $G.P.$ is $x^{3}, x^{5}, x^{7} \ldots .$
Here, $a=x^{3}$ and $r=x^{2}$
$S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}=\frac{x^{3}\left[1-\left(x^{2}\right)^{n}\right]}{1-x^{2}}=\frac{x^{3}\left(1-x^{2 n}\right)}{1-x^{2}}$
Similar Questions
The third term of a $G.P.$ is the square of first term. If the second term is $8$, then the ${6^{th}}$ term is
The third term of a $G.P.$ is the square of first term. If the second term is $8$, then the ${6^{th}}$ term is
If $y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x = $
If $y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x = $
If $a,\;b,\;c,\;d$ and $p$ are different real numbers such that $({a^2} + {b^2} + {c^2}){p^2} - 2(ab + bc + cd)p + ({b^2} + {c^2} + {d^2}) \le 0$, then $a,\;b,\;c,\;d$ are in
If $a,\;b,\;c,\;d$ and $p$ are different real numbers such that $({a^2} + {b^2} + {c^2}){p^2} - 2(ab + bc + cd)p + ({b^2} + {c^2} + {d^2}) \le 0$, then $a,\;b,\;c,\;d$ are in
- [IIT 1987]
Find four numbers forming a geometric progression in which the third term is greater than the first term by $9,$ and the second term is greater than the $4^{\text {th }}$ by $18 .$
Find four numbers forming a geometric progression in which the third term is greater than the first term by $9,$ and the second term is greater than the $4^{\text {th }}$ by $18 .$
The value of $\overline {0.037} $ where, $\overline {.037} $ stands for the number $0.037037037........$ is
The value of $\overline {0.037} $ where, $\overline {.037} $ stands for the number $0.037037037........$ is