(d) 1
Given exp. = log10 \(\bigg(10^{\frac{1}{2}}\,10^{\frac{1}{4}}\,10^\frac{1}{8}...... to\,∞\bigg)\)
= log10 \(10^{\big(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......to\,∞\big)}\)
= \({\big(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......to\,∞\big)}\). log10 10 [Using loga xn = n loga x]
= \(\frac{\frac{1}{2}}{\big(1-\frac{1}{2}\big)}\) x 1 = 1
\(\big(\) Using sum of GP of infinite terms = \(\frac{a}{1-r}\big)\)