Question

So last night i was sitting about bored and got to thinking about summations

Answer 1

And....

Answer 2

ugh, missed a "k" lol

\[\Large\sum_{k=1}^{n}\frac{1}{k}=\frac{\sum_{i=1}^{n}\frac{\prod_{k=1}^{n}k}{i}}{\prod_{i=k}^{n}k}\]

Answer 3

this got me thinking on how to do:\[\sum\frac{1}{an+k}\]for a hypergeometric series

Answer 4

\[\large \prod_{i=1}^{n}ai+k=...\]
i dont have a good notations for it, but it follows a pattern related to the binomial thrm

\[ \prod_{i=1}^{4}ai+k=4!a^4+(1.2.3+1.2.4+1.3.4+2.3.4)a^3k\]\[+(1.2+1.3+1.4+2.3+2.4+3.4)a^2k^2\]\[+(1+2+3+4)ak^3+k^4\]

Answer 5

the coeffs pattern out to all the combos tha the n! uses ... if that makes any sense

Answer 6

\[y = \prod_{n=1}^{5}4n+3 \]
\[ln(y) = \sum_{n=1}^{5}ln(4n+3)\]

Answer 7

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