The sum of n terms of m A.P.s are S1, S2, S3, …, Sm. If  the first term and common difference are 1, 2, 3, …, m  respectively, then S1 + S2 + S3 + … + Sm =

We have, S1=(n/2)[2⋅1+(n−1)⋅1]S2=(n/2)[2⋅2+(n−1)⋅2]Sm=(n/2)[2⋅m+(n−1)⋅m]∴S1+S2+…+Sm=n(1+2+3…+m)+n(n−1)2×(1+2+…+m)=m(m+1)2n+n2−n2=m(m+1)2⋅n(n+1)2=14mn(m+1)(n+1)