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8. Sequences and Series
easy
$7, 7^2, 7^3, ….7^n $ નો સમગુણોત્તર મધ્યક ..... છે.
A
${7^{\frac{{n + 1}}{2}}}$
B
${7^{\frac{n}{2}}}$
C
${7^{\frac{{n - 1}}{2}}}$
D
$7^n$
Solution
$7, 7^2, 7^3, ….7^n $ નો સમગુણોત્તર મધ્યક $ = {({7.7^2}{.7^3}{….7^n})^{\frac{1}{n}}}\,$
$= (7^{1 + 2 + 3 + …. + n})^\frac{1}{n}$
$= {\left( {{7^{\frac{{n(n + 1)}}{2}}}} \right)^{\frac{1}{n}}} $
$= {7^{\frac{{n + 1}}{2}}}$
Standard 11
Mathematics
