Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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+50

Range of inverse harmonic mean of two integers

Today I was solving an exercise and one of the things I tried (which later turned out to be useless) involved considering the following: Is there a simple way to describe in terms of $n$ the range of ...
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1answer
237 views
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The root of summation function

This is a calculation I need for my statistics project Big edit: simplify the function $f(x)$ a lot. Define for $f(x)$, $x\geq 0$, $$ f(x):=\sum_{k=1}^\infty ...
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6answers
283 views
+200

Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$

Prove that $$(n!)\cdot(m!)^n|(mn)!$$ I can prove it using Legendre's Formula, but I have to use the lemma that $$ ...