Home
Class 11
MATHS
Prove that:3^(1/2)xx3^(1/4)xx3^(1/8)xx.....

Prove that:`3^(1/2)xx3^(1/4)xx3^(1/8)xx...=3`

Text Solution

Verified by Experts

`L.H.S. = 3^(1/2)xx3^(1/4)xx3^(1/8)+...`
`=3^(1/2+1/4+1/8+1/16...)`
Now, we will solve, `(1/2+1/4+1/8+1/16...)`
It forms a GP with first term, `a= 1/2` and common ratio, `r = 1/2`
So, Sum of the given series will be, `S = a/(1-r) = (1/2)/(1-1/2) = 1`
So, our expression becomes,
`3^(1/2+1/4+1/8...) = 3^1 = 3 = R.H.S.`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NCERT|Exercise EXERCISE 9.1|14 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 2.3|5 Videos

  • SETS

    NCERT|Exercise EXERCISE 1.5|7 Videos

Similar Questions

Explore conceptually related problems

Prove that 9^(1//3)xx9^(1//9)xx9^(1//27)xx...oo=3 .

Prove that 1^(1)xx2^(2)xx3^(3)xx xx n^(n)<=[(2n+1)/3]^(n(n+1)/2),n in N

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

Prove that 1^1xx2^2xx3^3xx...xn^nlt ((2n+1)/(3))^((n(+1))/(2)

The sum of the series (1)/(3)+(1)/(3^(2)xx2)+(1)/(3^(3)xx3)+(1)/(3^(4)xx4)+... is :

If L=-lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1))) , then the value of L^(4) is _____________.

Simplify: (((-2)/3)^(-2))^(3)xx(1/3)^(-4)xx3^(-1)xx1/6

Simplify 4^(1/3)xx[2^(1/3)xx3^(1/2)]divide9^(1/4)