Find the value of 5\(\frac{1}{2}\), 5\(\frac{1}{4}\), 5\(\frac{1}{8}\)

1.	Find the value of 5\(\frac{1}{2}\), 5\(\frac{1}{4}\), 5\(\frac{1}{8}\) … up to infinity.
Answer» We have 5^{\(\frac{1}{2}\)}. 5^{\(\frac{1}{4}\)}. 5^{\(\frac{1}{8}\)} … ∞ = 5[\(\frac{1}{2}\)+ \(\frac{1}{4}\) + \(\frac{1}{8}\) +⋯∞] = \(5\bigg[\frac{\frac{1}{2}}{1-\frac{1}{2}}\bigg]\) \(\bigg[\) ∴ \(\frac{1}{2}\) + \(\frac{1}{4}\) + \(\frac{1}{8}\) + ⋯ ∞ = \(\frac{\frac{1}{2}}{1-\frac{1}{2}}=1\bigg]\) = 5¹ = 5

Find the value of 5\(\frac{1}{2}\), 5\(\frac{1}{4}\), 5\(\frac{1}{8}\) … up to infinity.

Answer»

We have 5^{\(\frac{1}{2}\)}. 5^{\(\frac{1}{4}\)}. 5^{\(\frac{1}{8}\)} … ∞

= 5[\(\frac{1}{2}\)+ \(\frac{1}{4}\) + \(\frac{1}{8}\) +⋯∞]

= \(5\bigg[\frac{\frac{1}{2}}{1-\frac{1}{2}}\bigg]\)

\(\bigg[\) ∴ \(\frac{1}{2}\) + \(\frac{1}{4}\) + \(\frac{1}{8}\) + ⋯ ∞ = \(\frac{\frac{1}{2}}{1-\frac{1}{2}}=1\bigg]\)

= 5¹

= 5