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For (2^(2)+4^(2)+6^(2)+.......+(2n)^(2))...

For `(2^(2)+4^(2)+6^(2)+.......+(2n)^(2))/(1^(2)+3^(2)+......+(2n-1)^(2))` to exceed 1.01, the maximum value of n is-

A

99

B

100

C

101

D

150

Text Solution

Verified by Experts

The correct Answer is:
D
`(2^(2)(1^(2)+2^(2)+3^(2)+......+n^(2)))/[[1^(2)+2^(2)+3^(2)+.......+(2n)^(2)]-2^(2)(1^(2)+2^(2)+3^(2)+.....n^(2)))`
`((2^(2)n(n+1)(2n+1))/(6))/((2n(2n+1)(4n+1))/(6)-(2^(2)n(n+1)(2n+1))/(6))gt1.0`
`(2n+2)/(2n-1)gt1.01`
`1+(3)/(2n-1)gt1.01`
`2n-1gt300`
`nlt150.5`
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