\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2010\cdot2011}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(=1-\frac{1}{2011}\)

\(=\frac{2010}{2011}\)

1/1x2 + 1/2x3 + 1/3x4 + .... + 1/2010x2011 

=1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2010 - 1/2011 

= 1/1 - 1/2011 

=2010/2011

\(S=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2010.2011}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(S=1-\frac{1}{2011}\)

\(S=\frac{2010}{2011}\)

Phân tích: 1 / 1 x 2 = 1 - 1/2

1/2.3 = 1/2 - 1/3

. ....Bạn làm tương tự các số còn lại...

Ta được: 1 - 1/2 + 1/2 - 1/3 + ....+1/ 2010 - 1/2011

= 1 - 1/2011

= 2010/2011

= 2.(1 / 2.3 + 1 / 3.4 + ..... + 1 / x (x + 1) = 2007/2009

= 2.(1/2 - 1/3 + 1/3 - +.......+ 1/x - 1/x+1) = 2007/2009

= 2.( 1/2 - 1/x+1) = 2007/2009

= 1 - 1/x+1 =2007/2009

= 1/x+1 = 1/2009

=> x + 1 = 2009

=> x = 2008

Ta có: 2/2.3 + 2/3.4 + .... + 2/x.(x+1) = 2007/2009

=> 2.[1/2.3+1/3.4+.....+1/x.(x+1)]=2007/2009

=> 2.(1/2-1/3+1/3-1/4 + .... + 1/x - 1/x+1) = 2007/2009

=> 2.(1/2-1/x+1)=2007/2009

=>1/2 - 1/x+1 = 2007/2009 : 2

=> 1/2 - 1/x+1 = 2007/4018

=> 1/x+1 = 2007/4018 +1/2 

=> 1/x+1 = 

= 2.(1 / 2.3 + 1 / 3.4 + ..... + 1 / x (x + 1) = 2007/2009

= 2.(1/2 - 1/3 + 1/3 - +.......+ 1/x - 1/x+1) = 2007/2009

= 2.( 1/2 - 1/x+1) = 2007/2009

= 1 - 1/x+1 =2007/2009

= 1/x+1 = 1/2009

=> x + 1 = 2009

=> x = 2008

\(P=\left(1-\frac{2}{2.3}\right).\left(1-\frac{2}{3.4}\right).\left(1-\frac{2}{4.5}\right)...\left(1-\frac{2}{99.100}\right)\)

\(P=\frac{4}{2.3}.\frac{10}{3.4}.\frac{18}{4.5}...\frac{9898}{99.100}\)

\(P=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{98.101}{99.100}\)

\(P=\frac{1.2.3...98}{2.3.4...99}.\frac{4.5.6...101}{3.4.5...100}\)

\(P=\frac{1}{99}.\frac{101}{3}=\frac{101}{297}\)

đặt 2 ra ngoài rồi làm bt là được bn nhé

3S=1x2x3+2x3x3+...+39x40x3

3S=1x2x(3-0)+2x3x(4-1)+...+39x40x(41-38)

3S=1x2x4-1x2x0+2x3x4-2x3x1+.....+39x40x41-38x39x40

3S=39x40x41

S=39x40x41:3

S=13x40x41

S=21320

S = 1 x 2 + 2 x 3 + 3 x 4 + ... + 39 x 40

S = 2 + 6 + 12 + ... + 1560

Sau đó tự làm nhé !

khong phai the

S = 1 x 2 +2x3 + 3x4+... + 38x39+39x40  

3S= 1.2.3+2.3.3+3.4.3+...+38.39.3+39.40.3

3S=1.2.(3-0)+2.3(4-1)+...+38.39(40-37)

3S=0.1.2-1.2.3+1.2.3-2.3.4+...+37.39.39-38.39.40

3S=38.39.40

S=19760

S = 1 x 2 +2x3 + 3x4+... + 38x39+39x40
3S= 1.2.3+2.3.3+3.4.3+...+38.39.3+39.40.3
3S=1.2.﴾3‐0﴿+2.3﴾4‐1﴿+...+38.39﴾40‐37﴿
3S=0.1.2‐1.2.3+1.2.3‐2.3.4+...+37.39.39‐38.39.40
3S=38.39.40
S=19760

S = 1x2 + 2x3 + 3x4 + ... + 38x39 + 39x40

3S = 1x2x3 + 2x3x3 + 3x4x3 + ... + 38x39x3 + 39x40x3

3S = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... + 38x39x(40-37) + 39x40x(41-38)

3S = 1x2x3 + 2x3x4 -1x2x3 + 3x4x5-2x3x4 + ... + 38x39x40-37x38x39 + 39x40x41-38x39x40

S = 39x40x41 : 3

S = 21320