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8. Sequences and Series
easy
संख्याओं $3,\,{3^2},\,{3^3},\,......,\,{3^n}$ का गुणोत्तर माध्य है
A
${3^{2/n}}$
B
${3^{(n - 1)/2}}$
C
${3^{n/2}}$
D
${3^{(n + 1)/2}}$
Solution
(d) गुणोत्तर माध्य$ = {({3.3^2}{.3^3}{…….3^n})^{1/n}}$
$ = {({3^{1 + 2 + …….n}})^{1/n}}$
$ = {\left( {{3^{\frac{{n\,(n + 1)}}{2}}}} \right)^{1/n}}$
$ = {3^{\frac{{n + 1}}{2}}}$.
Standard 11
Mathematics