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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 ?

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 ?

Grade:12

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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).

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