nice inequality

hey how u write log(1+n.2^(n-1)/2) as log 1.log n.2^(n-1)/2..........i don think dats correct

ya..........srry itz wrong

dats okay even i make mistake.....infact i m born to make mistake

Hint: Apply AM-GM to the n numbers
1, 2, 2², 2³, . . ., 2^n-1

yes kaymant sir is right

@ Archana
I think u r totally wrong
The ans given by u (above) is totally fake and copied.

kk thanx for that compliment

here's my solution.
observe that
2^0+2^1+2^2+...+2^{n-1}=2^n-1
applying AM-GM to the LHS we have
\frac{2^n-1}{n}\ge2^{\frac{n(n-1)}{n}}

or 2^n \ge 1+ n.2^n-1

which is what we wanted