Câu hỏi của Hoàng Mai Lê

Question

Tính tổng : S = 1 . 2+ 2 . 3 + 3 . 4 + ....... + 99 . 100

Trần Quỳnh Mai · Accepted Answer

$S=1.2+2.3+3.4+...+99.100$

$\Rightarrow3S=1.2.3+2.3.3+3.4.3+...+99.100.3$

$\Rightarrow3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)$

$\Rightarrow3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100$

$\Rightarrow3S=99.100.101=999900\Rightarrow S=999900\div3=333300$

Vậy : $S=333300$Câu trả lời: $S=1.2+2.3+3.4+...+99.100$

$\Rightarrow3S=1.2.3+2.3.3+3.4.3+...+99.100.3$

$\Rightarrow3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)$

$\Rightarrow3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100$

$\Rightarrow3S=99.100.101=999900\Rightarrow S=999900\div3=333300$

Vậy : $S=333300$

Phương Trâm · Answer

$S=1.2+2.3+3.4+...+99.100$

$3S=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)$

$3S=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100$

$3S=99.100.101=999900$

$S=999900:3$

$\Rightarrow S=333300$Câu trả lời: $S=1.2+2.3+3.4+...+99.100$

$3S=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)$

$3S=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100$

$3S=99.100.101=999900$

$S=999900:3$

$\Rightarrow S=333300$