The sum of the series 11+12+14+21+22+24+31+32+34+… to n terms is

Given  series is   11+12+14+21+22+24+31+32+34+…+ntermsIet T4 be the  nth term of the  series  11+12+14+21+22+24+31+32+34+…  Then,  Tn=n1+n2+n4=n1+n22−n2=nn2+n+1n2−n+1=121n2−n+1−1n2+n+1=1211+(n−1)n−11+n(n+1)∴ T1=1211−11+1⋅2T2=1211+1⋅2−11+2⋅3T3=1211+2⋅3−11+3⋅4⋯⋯ ⋯⋯⋯⋯Tn=1211+(n−1)n−11+n(n+1)On  adding  all  these  equations,  we get ∑r=1n Tr=121−11+n(n+1)=n(n+1)2n2+n+1