abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange
2013年1月15日 · 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. …
The idea behind the sum of powers of 2 - Mathematics Stack …
2016年10月29日 · $2^{n+1} - 1 = 2^n + 2^{n-1} + 2^{n-2} . . . + 2^1 + 2^0$ Suppose we take 2^n in the sum. We know since these are powers of two, that the previous term will be half of 2^n, …
Decomposition of …
It's a little question about number theory : Remark that we have : $$2+2^2=2*3$$ $$2+2^2+2^{2^2}=2*11$$ $$2+2^2+2^{2^2}+2^{2^{2^2}}=2*32779$$ Do we have : …
linear algebra - If $A^2 = I$ (Identity Matrix) then $A = \pm I ...
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Prove that $1^3 + 2^3 + ... + n^3 = (1+ 2 + ... + n)^2$
$$2(1+2+\ldots+k)+(k+1)=(k+1)^2\;.$$ Do you know a simpler expression for $1+2+\ldots+k$? (Once you get the computational details worked out, you can arrange them more neatly than …
How to prove a formula for the sum of powers of $2$ by induction?
2015年3月8日 · Let's take that assumption and see what happens when we put the next item into it, that is, when we add $2^n$ into this assumed sum: $$2^{n-1+1}-1 + 2^n$$ $$= 2^{n} - 1 + …
arithmetic - What's wrong with this fake proof that $2+2=5 ...
2017年9月28日 · Case in point, $3^2=(-3)^2$ and, as isyoung points out, $0.5^2=(-0.5)^2$. So, this fake-proof is designed to have one side equal to $0.5^2$ but the other side equal to $( …
calculus - How to integrate $\int \sqrt {x^2+a^2}dx
2013年5月15日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
exponentiation - Why is $2^{2^2}$ so much less than $2^{2^{2^2 ...
2022年11月7日 · Now, you can think that we are calculating those giant numbers as $^{5}2$ solving the power tower from top to bottom, so that $^{4}2$ becomes the exponent of $^{5}2$ …
Commutator of $x$ and $p^2$ - Mathematics Stack Exchange
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