bằng 40 nha

= ( 40 - 39 ) + ( 38 - 37 ) + ( 36 - 35 ) + ... + ( 4 - 3 )+ ( 2 - 1 )

= 1 + 1 + 1 + ... + 1 ( Có 20 số 1 )

= 1 * 20 

= 20

Chúc bạn học tốt 😊

ai giúp mình trả lời câu này nhé!!!

20

1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ... + 37 + 38 - 39 - 40

= ( 1+2-3-4 ) + ( 5+6-7-8 ) + ... + ( 37+38-39-40)

= (-4) + (-4) +... + (-4)

= (-4) . 10 (DO CÓ 10 NHÓM)

= -40

Ta có: S = 1.2 + 2.3 + 3.4 +.....+ 37.38 + 38.39

=> 3S = 1.2.(3 - 0) + 2.3.(4 - 1) + .... + 37.38.(39 - 36) + 38.39.(40 - 37)

=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + .... + 38.39.40

=> 3S = 38.39.40

=> S = 38.39.40 / 3

=> S = 19760

3s=1*2*3+2*3*3+....+37*38*3+38*39*3

3S=1*2*(3-0) + 2*3*(4-1) + ...+37*38*(39-36) + 38*39*(40-37)

3S=1*2*3-1*2*0 + 2*3*4-1*2*3 + ...+38*39*40-37*38*39

3s=37*37*39-1*2*0

3S=37*38*39=54834

S=18278

=-4+4-8+8+...-40+40=0

đúng nhé bạn

a) \(A=2^{100}-2^{99}-2^{98}-...-2^2-2^1\)( Có 2 câu nên mình tính nhanh luôn nhé )

\(\Leftrightarrow A=2^{100}-\left(2^1+2^2+2^3+...+2^{98}+2^{99}\right)\)

\(A=2^{100}-\left(2^{100}-2^1\right)=2^{100}-2^{100}+2=2\)

b) \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{36.37.38}+\frac{1}{37.38.39}\)

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

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

\(=\left(\frac{1}{2}-\frac{2}{3}\right)+\left(\frac{2}{3}-\frac{3}{4}\right)+\left(\frac{3}{4}-\frac{4}{5}\right)+...+\left(\frac{1}{37.38}-\frac{1}{38.39}\right)\)

\(=\frac{1}{2}-\frac{2}{3}+\frac{2}{3}-\frac{3}{4}+\frac{3}{4}-\frac{4}{5}+...+\frac{1}{37.38}-\frac{1}{38.39}\)

\(=\frac{1}{2}-\frac{1}{38.39}=\frac{741}{1482}-\frac{1}{1482}=\frac{740}{1482}=\frac{370}{741}\)

\(=\left(40^2-31^2\right)-\left(39^2-32^2\right)+\left(38^2-33^2\right)-\left(37^2-34^2\right)+\left(36^2-35^2\right)\)

\(=\left(40-31\right)\left(40+31\right)-\left(39-32\right)\left(39+32\right)+\left(38-33\right)\left(38+33\right)-\)

\(\left(37-34\right)\left(37+34\right)+\left(36-35\right)\left(36+35\right)\)

\(=9.71-7.71+5.71-3.71+1.71\)

\(=\left(9-7+5-3+1\right).71=5.71=355\)