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lnsum.py
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lnsum.py
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def L(x, n):
s = 0
for i in range(1, n+1):
s += (1.0/i)*(x/(1.0+x))**i
return s
def L2(x, n):
s = 0
for i in range(1, n+1):
s += (1.0/i)*(x/(1.0+x))**i
value_of_sum = s
first_neglected_term = (1.0/(n+1))*(x/(1.0+x))**(n+1)
from math import log
exact_error = log(1+x) - value_of_sum
return value_of_sum, first_neglected_term, exact_error
def table(x):
from math import log
print '\nx=%g, ln(1+x)=%g' % (x, log(1+x))
for n in [1, 2, 10, 100, 500]:
value, next, error = L2(x, n)
print 'n=%-4d %-10g (next term: %8.2e '\
'error: %8.2e)' % (n, value, next, error)
table(10)
table(100)
table(1000)
def L3(x, epsilon=1.0E-6):
x = float(x)
i = 1
term = (1.0/i)*(x/(1+x))**i
s = term
while abs(term) > epsilon:
i += 1
term = (1.0/i)*(x/(1+x))**i
s += term
return s, i
def table2(x):
from math import log
for k in range(4, 14, 2):
epsilon = 10**(-k)
approx, n = L3(x, epsilon=epsilon)
exact = log(1+x)
exact_error = exact - approx
print 'epsilon: %5.0e, exact error: %8.2e, n=%d' % \
(epsilon, exact_error, n)
print '\n\n'
table2(10)