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How do I calculate this sum in terms of 'n'? I know this is a harmonic progression, but I can't find how to calculate the summation of it. Also, is it an expansion of any mathematical function? 1 ...

$ (n+1)^3 - n^3 = 3n^2+3n+1$ - so it is clear that the $n^2$ terms can be added (with some lower-order terms attached) by adding the differences of cubes, giving a leading term in $n^3$. The …

Nov 28, 2019 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and …

Aug 30, 2010 · There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm. The confusing point here is that the formula $1^x = 1$ is …

Jan 15, 2013 · Possible Duplicate: How do I convince someone that $1+1=2$ may not necessarily be true? I once read that some mathematicians provided a very length proof of $1+1=2$. Can …

Apr 28, 2020 · I'm self-learning Linear Algebra and have been trying to take a geometric approach to understand what matrices mean visually. I've noticed this matrix product pop up repeatedly …

You can just leave $q$ as an indeterminate; note that the expression is $$ q^0+q^1+\dots+q^n $$ and this means that, for $n=0$, it is just $q^0=1$. So the base step is true.

May 9, 2016 · Prove that the sequence $\ {1, 11, 111, 1111, .\ldots\}$ will contain two numbers whose difference is a multiple of $2017$. I have been computing some of the immediate …

This sum is called $H_n$ the $n$th"harmonic number" and has no known closed form.