Pi=4(1-1/3+1/5-1/7+1/9-.................) How many term is needed to determine its value to two decimal place?

Answer 1

We need 4*(1/n) to be significantly less than 0.01. Writing this as a formal inequality:

4/n < 0.01

Multiply both sides by 100:
400/n < 1
Hence
n> 400

That means we need about 200 terms.

Answer 2

If you stop say at 13, then you omit 1/15 -1/17 + 1/19 etc and it is easy to see that this sum is at most 1/15. Using this you could say that going up to 1/399, then your error is at most 1/401 times 4 as required. So you need 200 terms.