商の計算

1. print(18/3)
2. print(1/7)
3. print(20//3)
4. print(20%3)
5. print(-20//3)
6. print(-20%3)

6.0
0.14285714285714285
6
2
-7
1

1. print(1/(2+4) + 5/(7+8) + 6/(3+9))
2. print(2/(6+9) + 3/(7+8) + 4/(1+5))
3. print(2/(7+8) + 3/(6+9) + 4/(1+5))
4. print(4/(5-3) + 8/(2-1) + 9/(7-6))
5. print(4/(5-3) + 8/(7-6) + 9/(2-1))
6. print(6/(2-1) + 8/(7-5) + 9/(4-3))
7. print(6/(4-3) + 8/(7-5) + 9/(2-1))

1.0
1.0
1.0
19.0
19.0
19.0
19.0

1. print(1/(3*6) + 5/(8*9) + 7/(2*4))
2. print(5/(1*8) + 7/(2*4) + 9/(3*6))
3. print(5/(2*4) + 7/(1*8) + 9/(3*6))
4. print(5/(3*4) + 6/(8*9) + 7/(1*2))
5. print(8/(4*9) + 5/(3*6) + 7/(1*2))
6. print(5/(3*8) + 7/(4*6) + 9/(1*2))
7. print(5/(4*6) + 7/(3*8) + 9/(1*2))

1.0
2.0
2.0
4.0
4.0
5.0
5.0

1. print(((1*2+3-4+5)/6+7)/8+9)
2. print(9+8-7*(6+5)/(4+3*2+1))
3. print(9/12+7/68+5/34)
4. print(((86+2*7)**5-91)/3**4)
5. print((8*(97+6/2)**5+1)/3**4)

10.0
10.0
1.0
123456789.0
987654321.0

1. print(1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5))
2. print(1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5) +1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10))
3. print(10/(1*2*3)+10/(2*3*4)+10/(3*4*5))

0.8
0.9
2.25

$\displaystyle \frac{1}{1×2}=\frac{1}{1}-\frac{1}{2}、\frac{1}{2×3}=\frac{1}{2}-\frac{1}{3}$となり、最終的には1問目は$\displaystyle \frac{1}{1}-\frac{1}{5}$、2問目は$\displaystyle \frac{1}{1}-\frac{1}{10}$のように、n項までの合計は$\displaystyle 1-\frac{1}{n+1}$で計算することができます。

この延長で最後の項が、$\displaystyle \frac{1}{99×100}$ となっても、計算は簡単です。

$\displaystyle \frac{1}{1\times2\times3}=\frac{1}{1\times2}-\frac{1}{2\times3\times}、\frac{1}{2\times3\times4}=\frac{1}{2\times3}-\frac{1}{3\times4}となります。$

1. from decimal import Decimal,getcontext
2. getcontext().prec = 80
3. print(Decimal('1')/Decimal('49'))
4. print(Decimal('1')/Decimal('499'))
5. print(Decimal('1')/Decimal('4999'))
6. print(Decimal('1')/Decimal('49999'))
7. print(Decimal('1')/Decimal('499999'))

0.020408163265306122448979591836734693877551020408163265306122448979591836734693878
0.0020040080160320641282565130260521042084168336673346693386773547094188376753507014
0.00020004000800160032006401280256051210242048409681936387277455491098219643928785757
0.000020000400008000160003200064001280025600512010240204804096081921638432768655373107
0.0000020000040000080000160000320000640001280002560005120010240020480040960081920163840