I was trying to calculate value of pi using this formula:
I had written this code for finding it for a given n:
def pisum(n): sum=3.0 x=2.0 while (n>0): if n%2==1: sum=sum+(4/(x*(x+1)*(x+2))) else : sum=sum-(4/(x*(x+1)*(x+2))) x=x+2 n=n-1 return str(sum) It runs fine for n=0 and n=1 and gives output 3.0, 3.16666666667. But for n=50 the output should be 3.1415907698497954 but it is giving 2.85840923015. Why so much difference? Please help to correct if i had done something wrong.
The problem is that you are using n%2 in order to determine whether to subtract or add. It is not the amount of loops that you start with that should matter, but which loop you're in. To see that, try using your function for an odd number, e.g. 51 and you will see that it will give you a correct answer.
To explain further, if you start with n=50, you will initially subtract (4/(x*(x+1)*(x+2))) from 3 rather than add to it, but if you start with n=51, you will initially add.
If you modify your function as follows:
def pisum(n): sum = 3.0 x = 2.0 for i in range(n): if i % 2 == 0: sum = sum + (4 / (x * (x + 1) * (x + 2))) else: sum = sum - (4 / (x * (x + 1) * (x + 2))) x = x + 2 return str(sum) you will always get a correct result.
You made a small mistake.
One correct program:
def pisum(n): sum = 3. for i in xrange(2, 2*n+2, 2): sum += (4. if (i&2) == 2 else -4.)/i/(i+1)/(i+2) return sum Being more conservative with number of lines:
def pisum(n): return 3. + sum([(4. if (i&2) == 2 else -4.)/i/(i+1)/(i+2) for i in xrange(2,2*n+2,2)]) Mistake in yours: You are iterating on n in reverse, thus one time (odd value of n) you are calculating:
and for another value of n (even value apart from 0) you are calculating
