if[.] denotes greatest integer function ,then what is the value of limit n tends to infinite if the function is [a]+[2a]+[3a]+...[na]whole devided by square of n ?

Hi Basit,

Use the property [x] = x - {x}

You will get

a+2a+3a+......na - ({a}+{2a}+.....{na})

ie a*n*(n+1)/2 - ({a}+{2a}+...{na})

as limit n tends to infinity, first term will tend to a/2, and then term in the brackets will tend to n (which is divided by n^2) and hence will tend to 0.

So answer is a/2.

Regards,

Ashwin (IIT Madras).