Question

[׺°”˜ﾟ°☆Cold Girl☆° ﾟ˜”°º× ❥]

Tính: 1+3+6+10+...+1176+1225

Ai nhanh mik k

Answer 1

[T.Anh 2K7(siêu quậy)(тoáɴ๖ۣۜнọc)]

\(M=\frac{1.2}{2}+\frac{2.3}{2}+\frac{3.4}{2}+\frac{4.5}{2}+...+\frac{48.49}{2}+\frac{49.50}{2}=\frac{1.2+2.3+3.4+4.5+...+48.49+49.50}{2}\)

Dặt\(A=1.2+2.3+3.4+...+48.49+49.50\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+48.49.3+49.50.3\)

\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+48.49.\left(50-47\right)+49.50.\left(51-48\right)\)

\(=1.2.3+\left(2.3.4-1.2.3\right)+\left(3.4.5-2.3.4\right)+...+\left(48.49.50-47.48.49\right)+\left(49.50.51-48.49.50\right)\)

\(=\left(1.2.3+2.3.4+3.4.5+...+48.49.50+49.50.51\right)-\left(1.2.3+2.3.4+...+47.48.49+48.49.50\right)\)

\(\Rightarrow3A=49.50.51=124950\Rightarrow A=41650\)

Mà\(M=\frac{A}{2}\)

\(\Rightarrow M=\frac{41650}{2}=20825\)

Vậy M=20825

Mk đặt =M cho ngắn gọn