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