For `(2^2+4^2+6^2+...+(2n)^2)/(1^2+3^3+5^2+...+(2n-1)^2) to exceed 1.01 is`

(2^(2)+4^(2)+6^(2)+...+(2n)^(2))/(1^(2)+3^(3)+5^(2) +...+(2n-1)^(2))rarr exceed 1.01i

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-

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

If 2^(3)+4^(3)+6^(3)+.. .+(2 n)^(3)=k n^(2)(n+1)^(2) then k=

If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2) then k=

(1^(3)+2^(3)+...+n^(3))/(1+3+5+...+(2n-1))=((n+1)^( 2))/(4)

Lt_(n rarr oo)(1.3.5...(2n-1))/(2.4.6...(2n))=

1 ^(2) + 2^(2) + 3^(2) + . . . + n^(2) = (n (n + 1) (2 n + 1))/( 6)