Rút gọn.

\(B=\dfrac{x^{39}x^{36}x^{33}...x^31}{x^{40}x^{38}x^{36}...x^21}=\dfrac{x^{\left(39+36+33+...+3\right)}}{x^{\left(40+38+36+...+2\right)}}\)

ta có: \(39+36+33+...+3=\dfrac{\left(39+3\right)\left(\dfrac{39-3}{3}+1\right)}{2}=273\)

\(40+38+36+....+2=\dfrac{\left(40+2\right)\left(\dfrac{40-2}{2}+1\right)}{2}=420\)

=> \(B=\dfrac{x^{273}}{x^{420}}=\dfrac{1}{x^{147}}\)

Tương tự như B => \(A=\dfrac{x^{4560}}{x^{496}}=x^{4064}\)

Ta có:

\(B=\dfrac{x^{\left(39+36+33+....+3\right)}}{x^{\left(40+38+36+....+2\right)}}\)

\(39+36+33+....+3=\dfrac{\left(39+3\right)\left(\dfrac{39-3}{3}+1\right)}{2}=273\)

\(40+38+36+....+2=\dfrac{\left(40+2\right)\left(\dfrac{40-2}{2}+1\right)}{2}=420\)

\(\Rightarrow B=\dfrac{x^{273}}{x^{420}}=\dfrac{1}{x^{147}}\)

tương tự => \(A=\dfrac{x^{4560}}{x^{496}}=x^{4064}\)

@lê thị hương giang

\(A=\frac{x^{39}+x^{36}+x^{33}+...+x^3+1}{x^{40}+x^{38}+x^{36}+...+x^2+1}\)

Đặt \(C=x^{39}+x^{36}+x^{33}+...+x^3+1\)

\(x^3.C=x^{42}+x^{39}+x^{36}+...+x^3\)

\(\left(x^3-1\right)C=x^{42-1}\)

\(C=\frac{x^{42}-1}{x^3-1}\)

Đặt \(D=x^{40}+x^{38}+x^{36}+....+x^2+1\)

\(x^2.D=x^{42}+x^{40}+x^{38}+x^{36}+....+x^2\)

\(\left(x^2-1\right).D=x^{42}-1\)

\(D=\frac{x^{42}-1}{x^2-1}\)

Ta có :

\(C:D=\frac{x^{42}-1}{x^3-1}:\frac{x^{42}-1}{x^2-1}\)

\(C:D=\frac{x^2-1}{x^3-1}\)

\(C:D=\frac{x+1}{x^2+x+1}\)

Ta có : \(A=C:D=\frac{x+1}{x^2+x+1}\)

Vậy ...........

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

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