Help Calculating Pi using Arctangent formula

  • #1

Homework Statement

Using the Arctangent formula
pi = 16 * arctan (1 / 5) - 4*arctan(1 / 239) to calculate the value of pi to 53 significant digits.

Homework Equations

The power series of arctangent(x) is = x − x^3/3 + x^5/5 − x^7/7 + x^9/9...

The Attempt at a Solution


I attempted this question on MAPLE 13(shown above), but I get an obvious incorrect answer 3.17... instead of 3.14...

Am i using the formula correctly? I've double checked the values and don't think I missed an exponent or inserted the wrong sign.

-Thanks in advance.
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  • #2
I'm not familiar with Maple, so I can't tell you what it's doing. However, using the same methid in Mathematica, I get 3.14... as expected, so I assume there is something odd about the way you've told Maple to calculate it...perhaps enclosing everything after "evalf" in a pair of brackets might change things?

In any case, I'm not sure you need terms all the way up to [itex]x^{51}[/itex] to get an accuracy of 53 decimal places. Use the remainder theorem for Taylor expansions to figure out how many terms you actually need.

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