answer=0
for i in range (11):
k=i
x = (-1**k) / ((2 * k) + 1)
answer+=x
answer=4*answer
print(answer)
output: -8.723498311114408
it should be close to 3.14
**
has precedence over -
(see the docs), hence -1 ** k
evalutes to -(1 ** k)
which is of course not what you meant.
Change x = (-1 ** k) / ((2 * k) + 1)
to x = (-1) ** k / ((2 * k) + 1)