Question

36. Find the sum of the infinite geometric series if it exists.
1+\frac{3}{2}+\frac{9}{4}+\frac{27}{8}+\cdots

Answer 1

Answer:

$=2\times \left( \frac{3}{2} \right)^{n+1} -2$

Step-by-step explanation:

$1+\frac{3}{2} +\frac{9}{4} +\frac{27}{8} +\cdots$

$=1+\left( \frac{3}{2} \right)^{1} +\left( \frac{3}{2} \right)^{2} +\cdots +(\frac{3}{2})^n$

$=\frac{1-\left( \frac{3}{2} \right)^{n+1} }{1-\frac{3}{2} }$

$=-2\times \left( 1-\left( \frac{3}{2} \right)^{n+1} \right)$

$=2\times \left( \left( \frac{3}{2} \right)^{n+1} -1\right)$