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bio website linkedin.com/in/gt6989b
location New York, NY
age 36
visits member for 3 years, 3 months
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May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
The only thing i can think about - prove that the sequence of terms is a Cauchy sequence. This only requires differences between successive terms.
May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
Numerically, converges to about $0.405284735 \approx \ln(1.5)$
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
nice and elegant
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
They do, you just have to express $\cos \theta$ in terms of $a_x, a_y, b_x, b_y$ and do the arithmetic.
May
1
comment How to find the full Taylor expansion of the following:
@user88595 fixed...
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
Well, you claimed it's a proof -- before we show that, it's not really a proof, is it?
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
Well, if $\vec{a} = a_x \hat{i} + a_y \hat{j}$, by definition, $$\left| \vec{a} \right| = \vec{a} \cdot \vec{a} = a_x^2 + a_y^2.$$
May
1
comment How to find the full Taylor expansion of the following:
@Frumpy partial fractions should reduce denominator to degree 1
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
I don't understand why this is a proof of geometric and algebraic equivalence. Algebraically, you argued $$\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y.$$ Geometrically, you argued that $$\vec{a} \cdot \vec{b} = \left| \vec{a} \right| \cdot \left| \vec{b} \right| \cos \theta = \sqrt{a_x^2 + a_y^2} \sqrt{b_x^2 + b_y^2} \cos \theta. $$ Why are they the same???
Apr
30
comment Ball Probability help
@user3335209 from (B) you found $\mathbb{P}[\text{same color}] = 14/45$. They must be either same or different, so $$\mathbb{P}[\text{same color}] + \mathbb{P}[\text{different color}] = 1$$
Apr
28
comment A linear growth model with immigration
@Danny yes, $o(h)$ includes any constant factor...
Apr
28
comment A linear growth model with immigration
@Danny $o(h)$ and $-o(h)$ is the same thing.
Apr
28
comment What does “Formulate the system of equations for a finite difference discretisation of the problem” mean?
What is meant by the question is, find the set of linear equations one would need to solve to get the numerical approximation to the problem you described via the method of finite differences.
Apr
24
comment Complicated but easy problem solving?
For the purpose of this problem, 03 is a more convenient representation than plain 3
Apr
24
comment Complicated but easy problem solving?
@AndréNicolas misread the problem, was counting numbers with 3 not actual occurrences. Fixed now.
Apr
24
comment Complicated but easy problem solving?
@gnasher729 fixed, thanks
Apr
13
comment Joint Probability Distribution Function
@Did is that integral not the probability that X=Y.
Apr
9
comment Logarithmic Equations and solving for the variable
@ajotatxe I'm sorry, I revised a couple of times, not sure if your remark is still relevant?
Apr
9
comment Logarithmic Equations and solving for the variable
+1 for thinking about the problem before posting here.
Apr
9
comment Need to check answer-Factoring out from surds
I think he meant $n^{3/2}$ not $n^3/2$