Parth Kohli
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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. Apr 21 answered Find $[3T^{n+2} + 3T^{n+1} + 3T^{n}]_{B}$ where $T(a,b,c) = (b,c,a)$ Apr 19 answered Prove $\sum _{k=2}^{n} k(k-1) {n \choose k}=n(n-1)2^{n-2}$ Jan 6 revised Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds. added 188 characters in body 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 6 answered Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds. 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 2 awarded algebra-precalculus 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. Jan 1 answered The value of the polynomial at given point. Nov 23 awarded Nice Answer Nov 8 comment prove polynomial division for any natural number Do you know the properties of the complex cube roots of unity? Oct 25 awarded Good Answer 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 answered Permutation in which the $A's$ appear together in a block of $4$ letters or the $B's$ appear together in a block of $3$ letters 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? Oct 1 awarded Popular Question 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.