Đặt A = 1.2 + 2.3 + 3.4 + ... + 99.100

=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3

=> 3A = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98)

=> 3A = 1.2.3 - 0 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + 99.100.101 - 98.99.100

=> 3A = 99.100.101

=> A = 99.100.101 : 3

=> A = 333300

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}\)

\(=1-\frac{1}{2006}\)

\(=\frac{2005}{2006}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}\)

= \(1-\frac{1}{2006}\)

= \(\frac{2005}{2006}\)

3M = 1.2.3 + 2.3.(4-1)  +..+  99.100.(101-98)

3M = 1.2.3 + 2.3.4 - 1.2.3 + .... + 99.100.101 - 98.99.100

3M = 99.100.101 = 999900

M  = 333300

333300

tick nha,nha!!!!!!!!!!!!!!!!!!!!!

Ta có : M = 1.2 + 2.3 + 3.4 + ..... + 212.213

=> 3M = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 212.213.214

=> 3M = 212.213.214

=> M = 212.213.214/3

=> M = 3221128

Câu a:

A = 1.2 + 2.3 + 3.4 + ...+ 99.100

3A = 1.2.3 + 2.3.3 +..+ 99.100.3

1.2.3 = 1.2.3

2.3.3 = 2.3(4 - 1) = 2.3.4 - 1.2.3

3.4.4 = 3.4(5 - 2) = 3.4.5 - 2.3.4

.............................................................

99.100.3 = 99.100.(101 - 98)=99.100.101-98.99.100

Cộng vế với vế ta có:

3A = 99.100.101

A = 99.100.101 : 3

A = 333300

Câu b:

1.3 + 3.5 + 5.7 + ..+ 97.99

6.A = 1.3.6 + 3.5.6 + 5.7.6 + ...+ 97.99.6

1.3.6 = 1.3.(5 + 1) = 1.3.5 + 1.3.1

3.5.6 = 3.5.(7 - 1) = 3.5.7 - 1.3.5

5.7.6 = 5.7.(9 - 3) = 5.7.9 - 3.5.7

.......................................................

97.99.6 = 97.99.(101 - 95) = 97.99.101-95.97.99

Cộng vế với vế ta có:

6A = 1.3.1 + 97.99.101

A = (1.3.1 + 97.99.101) : 6

A = (3 + 9603.101) : 6

A = (3+ 969903) : 6

A = 969906 : 6

A = 161651

kết quả là:2727117120

HOC QUA NHUNG QUEN MAT ROI 

Đặt A=1x2+2x3+3x4+.......+1999x2000

3xA=1x2x3+2x3x3+3x4x3+...........+1999x2000x3

3xA=1x2x3+2x3x(4-1)+............+1999x2000x(2001-1998)

3xA=1x2x3+2x3x4-1x2x3+...........+1999x2000x2001-1998x1999x2000

3xA=1999x2000x2001

A=1999x2000x2001:3

A=2666666000

\(A=\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{2007.2009}\)

\(2.A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2007.2009}\)

\(2.A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2007}-\frac{1}{2009}\)

\(2.A=1-\frac{1}{2009}=\frac{2008}{2009}\)

A=1004/2009