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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
S=1.2+2.3+...+39.40
3S=1.2.(3 - 0)+2.3.(4 - 1)+...+39.40.(41 - 38)
3S=1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 +...+ 39.40.41 - 38.39.40
3S=39.40.41
S=13.40.41
S=21320
D=1.2+2.3+3.4+..+19.20
=>3D=1.2.3+2.3.3+3.4.3+...+19.20.3
=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=2660
vậy D=2660
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
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{100.101}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{100}-\frac{1}{101}\)
\(=1-\frac{1}{101}\)\(=\frac{101}{101}-\frac{1}{101}\)
\(=\frac{100}{101}\)
3S = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) +...+ 99.100.(101 - 98)
3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +...+ 99.100.101 - 98.99.100
3S = 99.100.101
3S = 999900
S = 333300
M =1/1.2+1/2.3+1/3.4+.......+1/2019.2020
=1-1/2+1/2-1/3+1/3-1/4+.......-1/2019+1/2019-1/2020
=1-1/2020
=2019/2020
