MCQ
$\lim_{n \rightarrow \infty} \left(\frac{2}{3}+\left(\frac{2}{3}\right)^2+\left(\frac{2}{3}\right)^3+.........+\left(\frac{2}{3}\right)^n\right)=$...........
- A$1$
- ✓$2$
- C$\frac{1}{2}$
- Dએક પણ નહી.
$\lim_{n \rightarrow \infty} \left(\frac{2}{3}+\left(\frac{2}{3}\right)^2+.........+\left(\frac{2}{3}\right)^n\right)$
$=\lim_{n \rightarrow \infty}\frac{\frac{2}{3}\left[(\frac{2}{3})^n-1\right]}{\frac{2}{3}-1}$ $\because \frac{r(r^n-1)}{r-1}$ સુત્ર મુજબ .
$=\lim_{n \rightarrow \infty} -2\left[(\frac{2}{3})^n-1\right]$
$= -2\left((0)-1\right)$
$ =2$
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