ta co tu suy nghi 

chuẩn CMNR ;+

Cách 1:

 A = \(\frac{2}{1.2.3}\)+ \(\frac{2}{2.3.4}\)+ \(\frac{2}{3.4.5}\)+ .... + \(\frac{2}{36.37.38}\)+ \(\frac{2}{37.38.39}\)

A = \(\frac{3-1}{1.2.3}\)+ \(\frac{4-2}{2.3.4}\)+ \(\frac{5-3}{3.4.5}\)+ ... + \(\frac{38-36}{36.37.38}\)+ \(\frac{39-37}{37.38.39}\)

A = ( \(\frac{3}{1.2.3}\)- \(\frac{1}{1.2.3}\) )+ ( \(\frac{4}{2.3.4}\)-\(\frac{2}{2.3.4}\)) + ... + (\(\frac{38}{36.37.38}\)- \(\frac{36}{36.37.38}\)) + (\(\frac{39}{37.38.39}\)- \(\frac{37}{37.38.39}\))

A = ( \(\frac{1}{1.2}\)- \(\frac{1}{2.3}\)) + (\(\frac{1}{2.3}\) -\(\frac{1}{3.4}\) ) + ... + ( \(\frac{1}{36.37}\)- \(\frac{1}{37.38}\)) + ( \(\frac{1}{37.38}\)- \(\frac{1}{38.39}\))

A = \(\frac{1}{1.2}\)+ (-\(\frac{1}{2.3}\)+ \(\frac{1}{2.3}\)) + (-\(\frac{1}{3.4}\)+ \(\frac{1}{3.4}\)) + ..... + ( -\(\frac{1}{37.38}\)+\(\frac{1}{37.38}\)) - \(\frac{1}{38.39}\)

A = \(\frac{1}{1.2}\)+ 0 + 0 + 0 +... + 0 - \(\frac{1}{38.39}\)

A = \(\frac{1}{1.2}\)- \(\frac{1}{38.39}\)= \(\frac{741}{1482}\)- \(\frac{1}{1482}\)= \(\frac{740}{1482}\)=\(\frac{370}{741}\)

:)))) :>>> :+ := :- :

185/741

\(A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+....+\dfrac{1}{37.38.39}\)

\(A=\dfrac{1}{2}.\left(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+....+\dfrac{2}{37.38.39}\right)\)\(A=\dfrac{1}{2}\left(\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+....+\dfrac{39-37}{37.38.39}\right)\)

\(A=\dfrac{1}{2}.\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+.....\right)\)

Ta có :

\(S=1.2+2.3+...+39.40\)

\(\Rightarrow3S=1.2.3+2.3.3+....+39.40.3\)

\(\Rightarrow3S=1.2.\left(3-0\right)+2.3.\left(4-1\right)+....+39.40.\left(41-38\right)\)

\(\Rightarrow3S=1.2.3-0.1.2+2.3.4-1.2.3+.....+39.40.41-38.39.40\)

\(\Rightarrow3S=39.40.41\)

\(\Rightarrow S=\frac{38.39.40}{3}=21320\)

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

x=21320

S = 21320

Ta có:
S = 1x2 + 2x3 + 3x4 + ...+ 38x39 + 39x40
S x 3 = 1x2x3 + 2x3x3 + 3x4x3 +… + 38x39x3 + 39x40x3
S x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... + 38x39x(40-37) + 39x40x(41-38)
S x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 38x39x40 - 37x38x39 + 39x40x41 - 38x39x40.
S x 3 = 39x40x41
S = 39x40x41:3= 21320

ta có: S=2+6+12+1482+1560

 S=3062

chúc bạn học giỏi,nhớ k cho mình

1 x 2 +2 x 3 x 4 + 38 x 39 +39 x 40=

2 + 2 x 4 + 38 x 39 + 39 x 40=

2 + 8 +38 x 39 +39 x40=

2 + 8 + 1482 + 39 x 40=

2 + 8+ 1482 + 1560=

10 +1482 +1560 =

1492 +1560 = 3052

Ta có:
S = 1x2 + 2x3 + 3x4 + ...+ 38x39 + 39x40
S x 3 = 1x2x3 + 2x3x3 + 3x4x3 +… + 38x39x3 + 39x40x3
S x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... + 38x39x(40-37) + 39x40x(41-38)
S x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 38x39x40 - 37x38x39 + 39x40x41 - 38x39x40.
S x 3 = 39x40x41
S = 39x40x41:3= 21320

Đặt A = 1.2 + 2.3 + 3.4 + ... + 38.39 + 39.40

=> 3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 38.39.(40 - 37) + 39.40.(41 - 38)

           = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 38.39.40 - 37.38.39 + 39.40.41 - 38.39.40

           = 39.40.41 = 63960

=> A = 63960 : 3 = 21320

1 x 40 x (2 x 2) + (3x2) + (4x2) +...+ ( 39 x 2)

1 x 40 x (2 + 3 + 4 + .... + 39) x 2

40    x 779 x 2

31160 x 2

62320

k nha