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a=1.2+2.3+3.4+4.+....+200.201
3A = 1.2.(3 - 0) + 2.3.(4 - 1) + .... + 200.201.(202 - 199)
3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + .... + 200.201.202
3A = 200.201 . 202
A = 2706800
\(A=1.2+2.3+3.4+...+200.201\)
\(\frac{1}{A}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{200.201}\)
\(\frac{1}{A}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{200}-\frac{1}{201}\)
\(\frac{1}{A}=\frac{1}{1}-\frac{1}{201}=\frac{200}{201}\)
\(A=1:\frac{200}{201}=\frac{1.201}{200}=\frac{201}{200}\)
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
tính s = 1/2.3 - 2/3.4 + 3/4.5 - 4/5.6+......+ 199/200.201 - 200/201.202
các bạn giúp minh nhanh với
D=1.2+2.3+3.4+...+2017.2018
=>3D=1.2.3+2.3.3+3.4.3+...+2017.2018.3
=>3D=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+2017.2018.(2019-2016)
=>3D=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+2017.2018.2019-2016.2017.2018
=>3D=\(\frac{2017.2018.2019}{3}\)
=>D=2739315938
3C=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2014.2015.(2016-2013)
3C=2014.2015.2016
C=2014.2015.2016:3
D=1.2+2.3+3.4+...+99.100
=>3D=1.2.3+2.3.3+3.4.3+...+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=999900
=>D=333300
Đặt S= 1.2 + 2.3 + 3.4 + ...+ 99.100
3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101 3S = 3.33.100.101
S=33.100.101= 333300
D= 1.2 + 2.3 + 3.4 + ............. + 90.91
3D = 1.2.3 + 2.3.3 + 3.4.3 + .... + 90.91.3
3D = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 90.91.(92 - 89)
3D = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 90.91.92 - 89.90.91
3D = 90.91.92
D = 90.91.92 : 3 = 251160
Ta có : S = 1.2 + 2.3 + 3.4 + ..... + 32.33
=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 32.33.34
=> 3S = 32.33.34
=> S = \(\frac{32.33.34}{3}=11968\)
2706800 chắc chắn bạn nhé