Linked Questions

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2answers
5k views

Two divergent series such that their product is convergent

I faced a series question it goes something like give an example of 2 divergent series such that when the 2 series are multiplied to each other, the new series becomes convergent, although it looks ...
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1answer
2k views

How to solve this operation research problem using dual simplex method?

Maximize $$ z = 2x_1 -x_2 +x_3$$ Subject to constraints $$2x_1 + 3x_2 -5x_3 \ge 4$$ $$-x_1 +9x_2 -x_3 \ge 3$$ $$4x_1 +...
1
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4answers
355 views

What's the largest term in a converging series?

Although it's quite a trivial question but is it always that the very first term in a converging series is the largest term of all the terms in that series ? Since if $\sum A_n$ converges, that is if ...
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1answer
1k views

How to find the area shared by 4 quadrants inside a square?

I was to find the blue area in this question : As described about how it's a square with 4 quadrants of same radius intertwined with each other, now to find the blue part area I thought about finding ...
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3answers
238 views

How do I prove that $\lim_{(x,y) \to (0,0)} \frac{2y^2}{\sqrt{x^2+xy}}$ exists?

Now I have learnt that to prove a function of 2 variables exists we must have the both the repeated limits as equal, which is $\lim_{(x=0,y\to0)}f(x,y) = \lim_{(x\to0,y=0)}f(x,y)$ , now in this case $...
1
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2answers
328 views

Difference between mutually exclusive events and independent events?

whats the basic difference between mutually exclusive events and independent events ? how do both associate with each other ? and can both of them occur simultaneously ?
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2answers
246 views

Prove that if $\sum a_n$ converges/diverges so does $\sum {a_n/s_n}$ converge/diverge accordingly

There was this question where it was given that $a_n > 0$ and $s_n = a_0 + a_1 + a_2 +..........+a_n$ and here I was to prove that if : $\sum a_n$ converges/diverges so does $\sum {a_n/s_n}$ ...
2
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4answers
114 views

What's the Summation formulae of the series $2*2^0 + 3*2^1 + 4*2^2 + 5*2^3…$?

I faced this question where I was asked to find a summation formulae for $n$ terms of $2*2^0 + 3*2^1 + 4*2^2 + 5*2^3.......$ I did try generalizing it with $$a_n = (n + 1)2^{n - 1}; n2^{n - 2}$$ but ...
1
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1answer
68 views

How do we integrate $xe^{x^2}$ in this differential equation?

Yeah I did try searching how to integrate $e^{x^2}$ and mostly I stumbled upon how a similar but not this function called Gaussian function $e^{-x^2}$ is un-integrable , now I was given to solve a ...
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2answers
59 views

How come it be $\frac{3}{2}A$ and not only $A$?

OK I admit I was too lazy to type this question so I took a screenshot , I got it from the site @brilliant.org where it asked in terms of $A$ what would be the 2nd summation equation ? The explained ...
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2answers
78 views

Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.

The question is as follows if $ABC$ is a triangle, with $AD$ as the internal angle bisector of $\angle A$ with $D$ at $BC$ and $B^{'}, C^{'}$ are reflection of points $B$ and $C$ in $AD$. Show that ...