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Apr
21
comment Find $[3T^{n+2} + 3T^{n+1} + 3T^{n}]_{B}$ where $T(a,b,c) = (b,c,a)$
I'm very new to linear algebra (about three days). So if I got some part of the terminology wrong, please comment.
Jan
6
comment Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds.
@Macavity Oh, how did I forget? That case was all that was running in my mind and I forgot to mention it. Editing in a second.
Jan
6
comment Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds.
Please comment if I've missed out on anything.
Jan
4
comment The value of the polynomial at given point.
$x = \sqrt 2 - 1 \Rightarrow x + 1 = \sqrt{2} \Rightarrow (x+1)^2 = 2$ and so on. This technique was taught to me in my early days.
Jan
1
comment The value of the polynomial at given point.
Here is the computation done by WolframAlpha, but you shouldn't have a problem doing it by hand.
Nov
8
comment prove polynomial division for any natural number
Do you know the properties of the complex cube roots of unity?
Oct
7
comment Which integers $a$, $b$ and $c$ satisfy the equation $a\sqrt{2} - b = c\sqrt{3}$?
(0, 0, 0) is the first answer that comes to mind.
Oct
7
comment Given that $x,y,z$ are positive reals such that $xyz=32$.What is the minimum value of $x^2+4xy+4y^2+2z^2$.
This was there in the VMC test yesterday, wasn't it?
Sep
29
comment Let $a\ne1$ be an nth root of identity, show $1+2a+3a^2+\dots + na^{n-1} = \frac{n}{a-1}$.
This technique is employed whenever you have an arithmetico-geometric series.
Sep
17
comment Proving $\sum_{n=0}^N n (n!) = (N+1)!-1$
Write $n\cdot n! = (n+1 - 1)\cdot n! = (n+1)! - n!$ and then it telescopes nicely. Standard technique.
Jan
4
comment Given $a+b+c$, Can I calculate $a^2+b^2+c^2$?
No. Are there any more details given? If $ab + bc + ca$ is given, for example, then you can use the relation $(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$.
Nov
3
comment Is zero odd or even?
That is a valid test too. Odd $-$ odd is always even. So zero is even.
Aug
31
comment Find the sum, if exists $\sum\limits_{n=1}^{\infty} \frac{(2n)!}{2^{2n}(n!)^2(n+1)}$
I'd just stick to Shubham's method.
Aug
2
comment What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
Do you happen to have a copy of Higher Algebra by Hall and Knight? It contains quite a few of these in the first chapter.
Jun
26
comment Trigonometry / Finding the exact value
Do you understand that that the cosine function obtains the same value every $2\pi$?
Jun
5
comment How do you solve this using only given values, logarithm rules and no calculator?
You can introduce $\log(2)$ easily. $\log(4) = 2\log(2)= 0.6021 $.
May
22
comment Inequality involving conjugate numerator/denominator pairs
Are you there? Chat is up now.
May
22
comment Inequality involving conjugate numerator/denominator pairs
I would explain the full process to you, but the chat is offline. You can cancel the $x^3$ as a start.
May
20
comment Inequality involving conjugate numerator/denominator pairs
Yes, that's just the wavy-curve method. It's just that you put alternate + and - between the intervals.
May
20
comment Inequality involving conjugate numerator/denominator pairs
Don't worry. Do you know how to solve $(x + 2)(x + 4)(x + 7) < 0$ otherwise, without expanding it into a polynomial?