Question

(4-1/n)+(7-2/n)+(10-3/n)+..............+up to n terms?

Answer 1

here we look
(4+7+10+...........upto n term)-1/n (1+2+3+...........upto nterm)
=> 4+7+10+..... are in Ap
so sum of these series=n/2{2x4+(n-1)3}
=n/2(5+3n)-------(1)
again
=>(1+2+3+......) are also in Ap
sum of these=n/2 (n+1)------(2)
now put (1) and (2) both above equation
=>n/2(5+3n)-1/n {n/2 (n+1)}
=> n/2(5+3n)-1/2(n+1)=2n+3n^2/2-1/2