MHB Calculate Sigma Sums in Excel for Large n

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Calculating sigma sums in Excel for large "n" can be effectively managed by utilizing the software's capabilities. Excel 2003 has a limit of approximately 64,000 rows per column, while Excel 2007 and 2010 can handle around 1,000,000 rows. Users can work around these limits by using multiple columns or sheets if necessary. Familiarity with functions like =SUM() and anchoring techniques is essential for efficiently producing partial sums. Overall, Excel is a viable tool for handling large sigma notation sums with the right approach.
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Is anyone familiar enough with excel to use it to find the sum in of sigma notation when "n" is large?

\Sigma^{40}_{k=1} \sqrt\frac{3k-3}{4}

Something like this?
 
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Is it a matter of familiarity or a matter of just doing it?

Excel 2003 limited one to ~64,000 "n" in any single column. You could get past it by using multiple columns or sheets.

Excel 2007 and 2010 are more in the ~1,000,000 range.

If you know how to anchor a =sum(), you should be able to produce the sequence of partial sums quite easily.

Still, I don't know how large you are talking.
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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