S=1/2+1/3+...+1/38+1/39,P=1/39+2/38+...+38/2+39/1 tính S/P
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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
S=1.2+2.3+...+39.40
3S=1.2.3+2.3.3+...+39.40.3
3S=1.2.(3-0)+2.3.(4-1)+...+39.40.(41-38)
3S=1.2.3-0.1.2+2.3.4-1.2.3+...+39.40.41-38.39.40
3S=39.40.41
S=13.40.41
S=21320
\(S=1.2+2.3+3.4+...+38.39+39.40\)
\(3\text{S}=1.2.3+2.3.\left(4-1\right)+...+38.39.\left(40-37\right)+39.40.\left(41-38\right)\)
\(3\text{S}=1.2.3+2.3.4-1.2.3+...+38.39.40-37.38.39+39.40.41-38.39.40\)
\(3\text{S}=39.40.41\)
\(S=\frac{39.40.41}{3}=21320\)
S = 1*2+2*3+3*4+...+38*39+39*40
=>3S = 1.2.3+2.3.3+3.4.3+.....+38.39.3+39.40.3
=>3S = 1.2.3+2.3.(4-1)+3.4.(5-2)+......+38.39.(40-37)+39.40.(41-38)
=>3S = 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
=>3S = 39.40.41
=>3S = 63960
=> S = 21320
Vậy S là 21320
\(3S=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+39\cdot40\cdot\left(41-38\right)\)
\(3S=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+39\cdot40\cdot41-38\cdot39\cdot40\)
\(3S=39\cdot40\cdot41\)
\(=>S=39\cdot40\cdot41:3=21320\)
S=1.2 + 2.3 + 3.4 +...+ 38.39 + 39.40
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) + 3.4.(5-2) +...+ 38.39.(40-37) + 39.40.(41-38)
3S=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
3S=(1.2.3 - 1.2.3)+(2.3.4 - 2.3.4)+(3.4.5 - 3.4.5)+...+(37.38.39 - 37.38.39)+(38.39.40 - 38.39.40)+39.40.41
3S=39.40.41
S=\(\frac{39.40.41}{3}\)
\(\Rightarrow\)S=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
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
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