Gujarati
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

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