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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

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

B

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

C

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

D

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)`
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