1057http://www.targetiit.com/iit-jee-forum/posts/box-function-20319.html
do sumthing similar..... :)
1) Find the sum of
[(1/3√4) +(1/3√5) +(1/3√6).............(1/3√1000000)]
[.] stans for G.I.F. 3√n denotes the cube root of n.
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1057
1708\hspace{-16}$Let $\mathbf{f(x)=x^{-\frac{1}{3}}}$ and Here $\mathbf{f(x)}$ is a Strictly Decreasing function for $\mathbf{x>0}$
is answer is = 14996
7There r many meaningless qs. d above one may be 1 of them.. but what can be done ...@Shubhodip & @ fahadnasir... :)
1by expansion,
\left(1\pm \frac{2}{3}\frac{1}{n} \right)^{3}>\left(1\pm\frac{1}{n} \right)^{2}
this leads to (taking seperate equations)
\frac{3}{2}\left[(n+1)^{\frac{2}{3}}-n^{\frac{2}{3}} \right]<\frac{1}{n^{\frac{1}{3}}}<\frac{3}{2}\left[(n)^{\frac{2}{3}}-(n-1)^{\frac{2}{3}} \right]
from this you can proceed easily to get 14996.....:)