Let be geometric means inserted between two positive numbers and

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

G_1,G_2,\dots,G_k

k

geometric means inserted between two positive numbers

a

and

b

. Which of the following equals the product

G_1G_2\dots G_k

? (a)

(ab)^{\frac{k+2}{2}}

(b)

a^{\frac{k-1}{2}}\,b^{\frac{k+1}{2}}

(c)

(ab)^{k/2}

(d)

(a+b)^k