Calculating a Sum in C: Finding the Error in Floating Point Precision?

[I like Serena]

If you multiply your result with 6 and find the square root and then the error,how could we explain why the forward method gives better results for smaller n??

Lucky bad rounding.

Suppose we do the calculation with 2 significant decimal digits for n=4.
Then we get:
forward: ((1+0.25)+0.11)+0.063 = 1.5
backward: 1+(0.25+(0.11+0.063)) = 1.4

As you can see, the forward result is closer to $\pi^2/6 \approx 1.64$.
That is because of the lucky bad rounding of 0.25 to 0.3 and of 0.063 to 0.1.

Note that after iteration n=4, the forward result does not increase anymore (the next term is 0.04). But the backward result keeps getting closer to the desired end result.

 

[mathmari]

Thank you very very much! ;) :D