Let f( n )= [ 1 4 + n 1000 ] , where [ x ] denote the integral part of x . Then the value of _ n=1 ¹⁰⁰⁰ f(n) is

Step-by-step solution

aligned & f(n)= [ 1 4 + n 1000 ] & _ n=1 ¹⁰⁰⁰ f(n)= [ 1 4 + 1 1000 ]+ [ 1 4 + 2 1000 ]+ .+ [ 1 4 + 1000 1000 ] aligned =[0.25+0.001]+[0.25+0.002]+ .+[0.25+1] We get ' 0 ' for all values of n from 1 to 750 . From n =750 , we get all the values as 1 . So, array rl _ n=1 ¹⁰⁰⁰ & f(n)=0+0+0+ .+ [ 1 4 + 750 1000 ]+ [ 1 4 + 751 1000 ]+ .[1.25] & =1+1+1+ .(251 times ) & =251 array