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visits member for 3 years, 3 months
seen Dec 17 at 4:26

Apr
8
comment Is $(A+B)^2 = A^2 + B^2$ if $A$ and $B$ are matrices
Moreover, you proved OP's statement is true iff $AB = -BA$.
Apr
7
comment show that if $\displaystyle\lim_{n \to \infty} f(n+x)=0$ then $\displaystyle\lim_{x \to \infty}f(x)=0$
Welcome to Math.SE! Could you please post some of your thoughts to approach the problem and we will be glad to give hints and comments.
Apr
3
comment Solving inequalities with absolute values on both sides
@Joseph By the way, formally, the intersection between sets is never zero, but rather is said to be empty.
Apr
3
comment Solving inequalities with absolute values on both sides
@Joseph please see the edit
Apr
3
comment Solving inequalities with absolute values on both sides
@Joseph yes, they go by intersection. The second inequality splits, e.g. into $(2x-1) + |1-x| \ge 3$ and $-(2x-1) + |1-x| \ge 3$.
Apr
3
comment Evaluate the geometric series or state that it diverges.
@Mahina You compute the terms by "plugging in" the values $k=1,2,3$ into the formula in the sum: $4\left(\frac{-1}{5}\right)^{4\cdot 1}, 4\left(\frac{-1}{5}\right)^{4\cdot 2}, 4\left(\frac{-1}{5}\right)^{4\cdot 3}$. Simplify these, and then you get first term to be $a$ and ratio to be $r$. Check that ratio of 2nd/1st and 3rd/2nd terms is the same.
Apr
3
comment Evaluate the geometric series or state that it diverges.
@Mahina Ignore? Why? Write out the first three terms, what are they?
Apr
3
comment Have some trouble with limits
Do you know about Taylor series? That would help a lot with (3) and (4). Factor the denominator of (2) at $a^3-b^3$ with $a = \sqrt[3]{x}, b= 1$.
Apr
2
comment Can a transcendental number be an infimum of a set of rationals?
@user2345215 i thought it is generally known that any non constant algebraic functions of 1 variable, applied to a transcendetal number, yield transcendental output.
Apr
2
comment what is the difference between $f(x;y)$ and $f(x|y)$?
@George that depends on the particular book you are looking at. Lots will use these notations to mean the same thing.
Apr
2
comment What is the equation for a tangent to the graph of $y=\arcsin(x/2)$ at the origin?
@Hannah see the edit
Apr
2
comment Counting Balls / Elementary Generating Functions
Yes, first problem's bin has $10 \cdot 5 = 50$ balls, the second has $10 + 8 \cdot 4 = 42$ balls.
Apr
2
comment What is the equation for a tangent to the graph of $y=\arcsin(x/2)$ at the origin?
I wonder why -1, look ok to me.
Apr
2
comment Notation for near optimal solution
@MPW hilarious :)
Apr
2
comment Notation for near optimal solution
Welcome to Math.SE, thanks for your question. Hope you stay around and contribute to the site. I haven't seen a standard notation for such things.
Apr
2
comment Can a transcendental number be an infimum of a set of rationals?
@MPW thank you, dumb typo, sorry
Apr
2
comment Can a transcendental number be an infimum of a set of rationals?
@Lubin see the edit, you just need to negate it.
Apr
1
comment How to compute the nth power of a matrix
As is clear from the above argument, it works as long as P is invertible, it doesn't rely on P being orthogonal
Apr
1
comment How to compute the nth power of a matrix
@RyanMcGaha Ryan, see the last update to the answer, I posted my numbers, do we agree?
Apr
1
comment How to compute the nth power of a matrix
@RecklessReckoner Typo, sorry, $P = \pmatrix{1 & -1\\-1 &2}$ and $P^{-1}$ is correct.