Question

How to prove that 3^1/2*3^1/4*3^1/8 ... = 3

Answer 1

Answer:

$3^{(\frac{1}{2}+{\frac{1}{4}+{\frac{1}{8}...................)$= 3

Step-by-step explanation:

Formula used:

Sum of infinite G.P

$a+ar+ar^2+ar^3...........=\frac{a}{1-r}$

provided |r| < 1

$3^{\frac{1}{2}}*3^{\frac{1}{4}}*3^{\frac{1}{8}}.................\\\\3^(\frac{1}{2}+{\frac{1}{4}+{\frac{1}{8}...................)$

$Now,\\\\{\frac{1}{2}+{\frac{1}{4}+{\frac{1}{8}...................}\\\\=\frac{\frac{1}{2}}{1-\frac{1}{2}}\\\\=\frac{\frac{1}{2}}{\frac{1}{2}}\\\\=1$

$3^{(\frac{1}{2}+{\frac{1}{4}+{\frac{1}{8}...................)}=3^1=3$