Home
Class 12
MATHS
If x gt 0, (x^(n))/(1+x+x^(2)+...+x^(2n)...

If `x gt 0`, `(x^(n))/(1+x+x^(2)+...+x^(2n))` is

A

` le (1)/(2n+1)`

B

` lt (2)/(2n+1)`

C

` ge (1)/(2n+1)`

D

` gt (2)/(2n+1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `x+(1)/(x) ge 2`,……..`x^(n)+(1)/(x^(n)) ge 2`
On adding `(x+(1)/(x))+(x^(2)+(1)/(x^(2)))+…+(x^(n)+(1)/(x^(n))) ge 2n`
`:. ((1)/(x^(n))+(1)/(x^(n-1))+..(1)/(x))+1+(x+x^(2)+...+x^(n))ge 1+2n`
`:.((1+x+...+x^(n-1)+x^(n))+x^(n+1)+x^(n+2)+....+x^(2n))/(x^(n))ge 1+2n`
`:.(x^(n))/(1+x+....+2^(2n)) le (1)/(1+2n)`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Comprehension|2 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Examples|37 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|222 Videos

Similar Questions

Explore conceptually related problems

If I_(n)=int_(0)^(1)(1+x+x^(2)+....+x^(n-1))(1+3x+5x^(2)+....+(2n-3)x^(n-2)+(2n-1)x^(n-1))dx,n in N, then the value of sqrt(I_(9)) is

Draw the graph of the function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(x^(2)-1) .

If (1 + ax)^(n) = 1 + 6x + 27/2 x^(2) + ...... + a^(n)x^(n) , then the values of a and n are respectively

If p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2++x^(n-1)) is a polomial in x , then find possible value of ndot

If p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2++x^(n-1)) is a polomial in x , then find possible value of ndot

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these

Let m,n be two positive real numbers and define f(n)=int_(0)^(oo)x^(n-1)e^(-x)dx and g(m,n)=int_(0)^(1)x^(m-1)(1-m)^(n-1)dx . It is known that f(n) for n gt 0 is finite and g(m, n) = g(n, m) for m, n gt 0. int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dx=

If x = sum_(n = 0)^(infty) cos ^(2n) theta, " "y = sum_(n = 0)^(infty) sin^(2n) theta and z = sum_(n = 0)^(infty) cos^(2n) theta sin^(2n)theta, 0 lt theta lt (pi)/(2) , then show that xyz = x + y + z [ Hint : use the formula 1 + x + x^(2) + x^(3) +... =(1)/(1 - x) , where |x| lt 1 ]