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The minimum value of n for which (2^(2)+...

The minimum value of n for which `(2^(2)+4^(2)+6^(2)+...+(2n)^(2))/(1^(2)+3^(2)+5^(2)+...+(2n-1)^(2)) lt 1.01`

A

is 101

B

is 121

C

is 151

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
C
`x/((2n(2n+1)(4n +1))/(6)-x) lt 1.01`
`2.01x lt (1.01) (2n(2n+1)(4n+1))/(6)`
`2.01. (4n(n+1)(2n+1))/(6) lt (1.01) (2n(2n+1)(4n+1))/(6)`
`2.01/1.01 lt (4n+1)/(2n+2) rArr n gt 150.5`
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