Home
Class 12
MATHS
Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)o...

Prove that `6^(1//2)xx6^(1//4)xx6^(1//8)oo=6.`

Text Solution

Verified by Experts

We have,
`6^(1//2)xx6^(1//4)xx6^(1//8)…oo`
`=6^([1//2+1//4+1//8+… "to"oo]`
`=6^([(1//2)//(1-1//2)])=6^(1)=6`
`[because1/2+1/4+1/8+…"to"oo=(1//2)/(1-1//2)=1]`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.6|11 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.7|4 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.4|13 Videos

  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

The value of the product 6^((1)/(2))xx6^((1)/(4))xx6^((1)/(8))xx6^((1)/(16))xx.... up to infinite terms is

The value of the infinite product 6(1)/(2)xx6^((2)/(4))xx6^((3)/(8))xx6(4)/(16)xx...

(4^(-1)xx3^(-1))-:6^(-1)

If x+(1)/(x)=a then prove that x^(6)+(1)/(x^(6)) =a^(6)-6a^(4) +9a^(2)-2 .

1/2xx 5/4 + 6/8 xx 10/9

Find the number of zeroes in the product 1^(1)xx2^(2)xx3^(3)xx4^(4)xx5^(5)xx6^(6)xx…xx49^(49)

Simplify each of the following using suitable property.(i)[(1)/(2)xx(1)/(4)]+[(1)/(2)xx6]