Đáp án: $S=34.35.12-2$
Giải thích các bước giải:
Ta có:
$S=2.3+3.4+4.5+...+34.35$
$\to 3S=2.3.3+3.4.3+4.5.3+...+34.35.3$
$\to 3S=2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+34.35.(36-33)$
$\to 3S=-1.2.3+2.3.4-2.3.4+3.4.5-3.4.5+4.5.6-....-33.34.35+34.35.36$
$\to 3S=-1.2.3+34.35.36$
$\to 3S=-1.2.3+34.35.12. 3$
$\to 3S=3(-1.2+34.35.12)$
$\to S=-1.2+34.35.12$
$\to S=-2+34.35.12$
$\to S=34.35.12-2$
