D=1.2+2.3+3.4+...+19.20

=>3D=1.2.3+2.3.3+3.4.3+...+19.20

=1.2.3+2.3(4-1)+3.4(5-2)+...+19.20(21-18)

=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+19.20.21-18.19.20

=19.20.21=7980

=>D=7980:3=2660

Vậy D=2660

C=1*2+2*3+3*4+...+98*99

C=2+6+12+...+9702

C=2+9702

C=9704

vay C=9704

D=(1*99+2*99+3*99+...+99*99)-(1*2+2*3+3*4+...+98*99)

D=(99+198+297+...+9801)-(2+6+12+...+9702)

D=(99+9801)-(2+9702)

D=9900-9704

D=196

vay D=196

ai di qua dong tinh thi nho h cho minh nhe

 3M = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 212.213.3 
Mà : 
1.2.3 = 1.2.3 
2.3.3 = 2.3.4 - 2.3.1 
3.4.3 = 3.4.5 - 3.4.2 
4.5.3 = 4.5.6 - 4.5.3 
............................. 
............................. 
............................ 
211.212.3 = 211.212.213 - 211.212.210 
212.213.3 = 212.213.214 - 212.213.211 

Cộng tất cả lại vế theo vế ---> 3M = 212.213.214 
---> M = 212.213.214/3 = 212.71.214 = 3221128

Gọi tổng trên là  A

\(3A=1.2.3+2.3.3+3.4.3+...+n.\left(n+1\right).3\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+n.\left(n+1\right).\left[\left(n+2\right)-\left(n-1\right)\right]\)

\(\Rightarrow3A=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5+...-\left(n-1\right).n.\left(n+1\right)+n.\left(n+1\right).\left(n+2\right)\)

\(\Rightarrow3A=n.\left(n+1\right).\left(n+2\right)\Rightarrow A=\frac{n.\left(n+1\right).\left(n+2\right)}{3}\)

tick nha

 S=1.2+ 2.3+.......+99.100 
Nhân cả 2 vế với 3, ta được: 
3S=1.2.3+ 2.3.3+ 3.4.3+ 4.5.3+...... 99.100.3 
= 1.2.3 + 2.3(4-1) + 3.4.(5-2) +...+ 99.100.(101-98) 
= 1.2.3 + 2.3.4 -1.2.3 + 3.4.5-2.3.4 +...+ 99.100.101-98.99.100 
= 99.100.101 
----> S = (99.100.101):3 
S = 333300 
Vậy S=333300 

de

A=1.2+2.3+3.4+.....+100.101

3A=1.2.3+2.3.3+3.4.3+..+100.101.3

3A=1.2.3+2.3.(4-1)+3.4.(5-2)......+100.101.(102-99)

3A=1.2.3+2.3.4-2.3.1+3.4.5-3.4.2+....+99.100.101-100.101.102

3A=100.101.102

3A=\(\frac{100.101.101}{3}\)

Ta có : A = 1.2 + 2.3 + 3.4 + ..... + 100.101

=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 100.101.102

=> 3A = 100.101.102

=> A = 100.101.102/3

=> A = 343400