Q6 of 104 Page 488

Prove that 9^1/3 × 9^1/9 × 9^1/27 × …..∞ = 3

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

∴Sum of the series in the exponent

∴L.H.S=9^1/2

=3=R.H.S

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

Find the sum of each of the following infinite series :

10 – 9 + 8.1 - ……∞

Find the sum of each of the following infinite series :

∞

Find the rational number whose decimal expansion is given below :

(i) (ii)

(iii)

Express the recurring decimal 0.125125125 …. = as a rational number.

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