Question

Prove that 91/3 × 91/9 × 91/27 × …..∞ = 3

Answer 1

L.H.S=9^1/3 × 9^1/9 × 9^1/27 × …..∞ 

=9^{(1/3)+(1/9)+(1/27)}+…∞ 

The series in the exponent is an infinite geometric series 

Whose, a = \(\frac{1}{3}\)

Sum of the series in the exponent 

∴L.H.S=91/2 

=3 = R.H.S 

Hence, Proved that 9^1/3 × 9^1/9 × 9^1/27 × …..∞ = 3