HW3.ipynb

Kernel: Python 3 (system-wide)

print ("#1")

#1

S = 0.0
for i in range(6):
    x = (-1) ** i / (i * 2 + 1)
    S += x
    print (x)

1.0
-0.3333333333333333
0.2
-0.14285714285714285
0.1111111111111111
-0.09090909090909091

S = 0.0
for i in range(100):
    x = (-1) ** i / (i * 2 + 1)
    S += x
print (S)

0.7828982258896384

S = 0.0
y = 1
for i in range(10):
    x = (-1) ** i / y
    S += x
    y += 2
    print (x,y)

1.0 3
-0.3333333333333333 5
0.2 7
-0.14285714285714285 9
0.1111111111111111 11
-0.09090909090909091 13
0.07692307692307693 15
-0.06666666666666667 17
0.058823529411764705 19
-0.05263157894736842 21

S = 0.0
y = 1
for i in range(100):
    x = (-1) ** i / y
    S += x
    y += 2
print (S)

0.7828982258896384

3.14 / 4

0.785

print("#2")

#2

S =1
N=1
D=1
for i in range(1,100):
    D = D * (2*i + 1)
    N = N * i
    S = S + N/D
print(2*S)

3.1415926535897922

import math

x = math.sqrt(2)
for i in range(10):
    P = (P * x) / 2
    x = math.sqrt(2.0 + x)
    print(2/P)

2.82842712474619
3.0614674589207183
3.121445152258052
3.136548490545939
3.1403311569547525
3.141277250932773
3.141513801144301
3.1415729403670913
3.141587725277159
3.1415914215111997