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8. Sequences and Series
easy
સમગુણોત્તર શ્રેણીમાં નિર્દેશિત પદોનો સરવાળો શોધો : ${{x^3},{x^5},{x^7}, \ldots }$ પ્રથમ $n$ પદ
A
$\frac{x^{3}\left(1-x^{2 n}\right)}{1-x^{2}}$
B
$\frac{x^{3}\left(1-x^{2 n}\right)}{1-x^{2}}$
C
$\frac{x^{3}\left(1-x^{2 n}\right)}{1-x^{2}}$
D
$\frac{x^{3}\left(1-x^{2 n}\right)}{1-x^{2}}$
Solution
The given $G.P.$ is $x^{3}, x^{5}, x^{7} \ldots .$
Here, $a=x^{3}$ and $r=x^{2}$
$S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}=\frac{x^{3}\left[1-\left(x^{2}\right)^{n}\right]}{1-x^{2}}=\frac{x^{3}\left(1-x^{2 n}\right)}{1-x^{2}}$
Standard 11
Mathematics
