Q. 64.0( 4 Votes )

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

Answer :

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

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