abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange
Jan 15, 2013 · The main reason that it takes so long to get to $1+1=2$ is that Principia Mathematica starts from almost nothing, and works its way up in very tiny, incremental steps. …
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Formula for sequence of 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, and so on (non ...
Apr 28, 2019 · I have been trying to figure out a formula for the sequence: 0, 0, 1, 1, 2, 2, 3, 3, 4, 4 It is not geometric and it is not arithmetic, I tried to apply these ...
Formula for $1^2+2^2+3^2+...+n^2$ - Mathematics Stack …
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
Exactly how does the equation n (n-1)/2 determine the number of …
Apr 2, 2017 · Plugging 4 into the equation we get 4(4-1)/2 = 12/2 = 6. So there are 6 possible combinations with 4 items. Applying the intuitive understanding of division as repeated …
General term formula of series 1/1 + 1/2 + 1/3 ... +1/n
I can give you a good approximation if you would prefer: $$\ln(n+1)\le\sum_{i=1}^n\frac1i\le\ln(n)+1$$ This is a rather tight upper limit and lower limit …
Writing 1+1= 2 in a complicated way - Mathematics Stack Exchange
I understand steps one and two, but when it comes to the third step, where he "cleans up" again, I get lost in thought. I would Google this, but I do not know the technical term, hence the title …
Prove $\\sin^2\\theta + \\cos^2\\theta = 1$ - Mathematics Stack …
Oct 6, 2014 · (Imagine bringing the blue segment down so it lies on top of part of the purple segment - $\sin^2\theta + \cos^2\theta = 1$ (since $\sin^2\theta + \cos^2\theta = 1^2$). Since …
Intuition behind the formula for $\\sum_{i=1}^n i^{2}$
Since you asked for an intuitive explanation consider a simple case of $1^2+2^2+3^2+4^2$ using a set of children's blocks to build a pyramid-like structure. First you arrange $16$ blocks in a …
Gamma function proof of gamma $\\;Γ(1/2) = \\sqrt \\pi\\;$
Feb 18, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …