Đáp án:
$S=48178$
Giải thích các bước giải:
$S=1.3+2.4+3.5+\cdots+51.53\\ S=1.(1+2)+2.(1+3)+3.(1+4)+\cdots+51.(1+52)\\ =\underbrace{1.2+2.3+3.4+\cdots+51.52}_A+\underbrace{1+2+3+\cdots+51}_B\\ A=1.2+2.3+3.4+\cdots+50.51.3+51.52\\ 3A=1.2.3+2.3.3+3.4.3+\cdots+50.51.3+51.52.3\\ =1.2.3+2.3.(4-1)+3.4.(5-2)+\cdots+50.51(52-49)+51.52.(53-50)\\ =1.2.3-1.2.3+2.3.4-2.3.4+3.4.5+\cdots-49.50.51+50.51.52-50.51.52+51.52.53\\ =51.52.53\\ =140556\\ \Rightarrow A=46852\\ B=1+2+3+\cdots+51\\ =\underbrace{(1+51)+(2+50)+\cdots+(25+27)}_{\text{25 cặp}}+26\\ =52.25+26\\ =1326\\ S=A+B=48178$
