Question:
Prove that $\left(1-\frac{1}{3}+\frac{1}{3^{2}}-\frac{1}{3^{3}}+\frac{1}{3^{4}} \ldots \infty\right)=\frac{3}{4}$
Solution:
It is Infinite Geometric Series.
Here, a = 1,
$r=\frac{\frac{-1}{3}}{1}=\frac{-1}{3}$
Formula used: Sum of an infinite Geometric series $=\frac{a}{1-r}$
$\therefore$ Sum $=\frac{1}{1-\frac{-1}{3}}=\frac{1 \times 3}{3+1}=\frac{3}{4}=$ R.H.S.
Hence, Proved that $\left(1-\frac{1}{3}+\frac{1}{3^{2}}-\frac{1}{3^{3}}+\frac{1}{3^{4}} \ldots \infty\right)=\frac{3}{4}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.