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May
5
answered Proving breath first traversal on graphs
May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
Moreover, it's easy to see it is an increasing sequence, you just need to show it is bounded above.
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
5
reviewed Approve How do I calculate the dimensions of this Frustum?
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
revised How to find the full Taylor expansion of the following:
added 27 characters in body
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
answered How to find the full Taylor expansion of the following:
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???
May
1
revised Geometric and algebraic definitions of the dot product , proof of equivalence?
added 213 characters in body
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
30
answered Finding values $a$ and $b$ which transforms a differential equation
Apr
30
answered Ball Probability help
Apr
30
revised Ball Probability help
added 27 characters in body
Apr
28
revised Simple linear regression prove variables are uncorrelated:
added 44 characters in body