đặt S=1.2.3+2.3.4+....+47.48.49

4S=1.2.3.(4-0)+2.3.4.(5-1)+...+47.48.49.(50-46)

4S=1.2.3.4-1.2.3+2.3.4.5-1.2.3.4+....+47.48.49.50-46.47.48.49

4S=47.48.49.50-1.2.3

S=(47.48.49.50-1.2.3):4

cool queen đúng rồi

\(M=1.2.3+2.3.4+3.4.5+...+47.48.49\)

\(4M=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+...+47.48.49.\left(50-46\right)\)

\(=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+47.48.49.50-46.47.48.49\)

\(=47.48.49.50\)

\(M=\frac{47.48.49.50}{4}=1381800\)

Dat A=1.2.3+2.3.4+3.4.5+...+98.99.100

      4A=1.2.3.4+2.3.4.4+3.4.5.4+...+98.99.100.4

      4A=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+...+98.99.100.(101-97)

       4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+98.99.100.101-97.98.99.100

        4A=98.99.100.101

         A=\(\frac{98.99.100.101}{4}\)

          A=24497550

Ung ho minh nha

Tick minh thi may man ca nam do!!!!!

Tick minh nha Dinh Duc Hung

Đinh Đức Hùng dg j đây

a: \(M=1\cdot2+2\cdot3+\cdots+2020\cdot2021\)

\(=1\left(1+1\right)+2\left(2+1\right)+\cdots+2020\left(2020+1\right)\)

\(=\left(1^2+2^2+\cdots+2020^2\right)+\left(1+2+\cdots+2020\right)\)

\(=\frac{2020\left(2020+1\right)\left(2\cdot2020+1\right)}{6}+\frac{2020\cdot2021}{2}\)

\(=\frac{2020\cdot2021\cdot4041+3\cdot2020\cdot2021}{6}=\frac{2020\cdot2021\cdot4044}{6}\)

\(=2020\cdot2021\cdot674=2751551080\)

b: \(N=1\cdot2\cdot3+2\cdot3\cdot4+\cdots+2019\cdot2020\cdot2021\)

\(=2\left(2-1\right)\left(2+1\right)+3\left(3-1\right)\left(3+1\right)+\cdots+2020\left(2020-1\right)\left(2020+1\right)\)

\(=2\left(2^2-1\right)+3\left(3^2-1\right)+\cdots+2020\left(2020^2-1\right)\)

\(=\left(2^3+3^3+\cdots+2020^3\right)-\left(2+3+\cdots+2020\right)\)

\(=\left(1^3+2^3+\cdots+2020^3\right)-\left(1+2+3+\cdots2020\right)\)

\(=\left(1+2+\cdots+2020\right)^2-\left(1+2+3+\cdots+2020\right)\)

\(=\left(2020\cdot\frac{2021}{2}\right)^2-2020\cdot\frac{2021}{2}=\left(1010\cdot2021\right)^2-1010\cdot2021\)

4A=4.[1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 + . . . . . . + 48.49.50] 
4A=1.2.3.4 +2.3.4.4 +3.4.5.4 +4.5.6.4 +.........+48.49.50.4 
4A=1.2.3.4 +2.3.4.(5-1) + 3.4.5.(6-2) +4.5.6(7-3)+....+ 48.49.50(51-47) 
4A=1.2.3.4 +2.3.4.5 --1.2.3.4 + 3.4.5.6--2.3.4.5 + 4.5.6.7-3.4.5.6+....+ 48.49.50.51--47.48.49.50 
4A =48.49.50.51 
A=(48.49.50.51)/4 

đáp số bài này là 1.499.400

Bạn ấn vào dòng chữ màu xanh Cho D =  1/1.2.3+1/2.3.4+....+1/37.38.39

\(C=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{38.39.40}=\frac{1}{2}\cdot\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{38.39}-\frac{1}{39.40}\right)=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{39.40}\right)=\frac{1}{2}\cdot\frac{599}{1200}=\frac{599}{2400}\)

khó à nha