I'm learning series and I wanted to check myself, whether or not I've done
correct convergence test. I have this series:
((n-1)/(n+1))**(n**2)
I applied function summation and got nothing. But in fact this series
converges, I checked that with ratio test.
So I decided to write function that implements ration test. It's quite
simple (draft) function. I assumed that series depends on variable n (I
didn't find way to find function arguments, I think I can do it with
something like recursive calls of method args, but I'm not sure). Here it
is:
def ratio_test(series, x=n):
"""Ratio test for testing series convergence"""
ratio_limit = abs((series.subs(x, n + 1)/series.subs(x, n)).limit(n,
oo))
if ratio_limit < 1:
return True
elif ratio_limit == 0:
return None
elif ratio_limit > 1:
return False
Tests:
a_n = (((n-1)/(n+1))**(n**2))
ratio_test(a_n)
Out: True
b_n = z**n/factorial(n)
ratio_test(b_n)
Out: True
c_n = factorial(n)*z**n
ratio_test(c_n)
Out: True
d_n = 1/n
ratio_test(d_n)
Out: None
e_n = t/(exp(t))
ratio_test(e_n, t)
Out: True
Should I contribute and put those functions for example in series module?
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