Question Number 10340 by konen last updated on 04/Feb/17

A=1×2 +2×4 +3×6+...+14×28  B=1×3 +2×3 +...+14×29  ⇒B=?

Commented bymrW1 last updated on 04/Feb/17

the definition of B is not clear.    do you mean   B=1×3 +2×5 +...+14×29 ?    if this is true, then  B=Σ_(n=1) ^(14) b_n =Σ_(n=1) ^(14) n(2n+1)  =2Σ_(n=1) ^(14) n^2 +Σ_(n=1) ^(14) n  =2×((14×(14+1)×(2×14+1))/6)+((14×(14+1))/2)  =((2×14×15×29)/6)+((14×15)/2)  =2030+105=2135