Question

Prove that $6^{\frac{1}{2}}\times 6^{\frac{1}{4}}\times 6^{\frac{1}{8}}.....\infty =6$

Answer 1

$=6^{\frac{1}{2}}{6}^{\frac{1}{4}}{6}^{\frac{1}{8}}..........\infty =6^{\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+........\infty }=6^{\frac{\frac{1}{2}}{1-\frac{1}{2}}}=6^{\frac{\frac{1}{2}}{\frac{1}{2}}}=6$