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2d
comment help with showing a series is divergent
I assume you want to divide by $n^2$. If you multiply the result is trivial. On the assumption you want to divide, after a short while $\ln n\gt e$.
2d
comment Finding the probability of that the first ball drawn at random was red given that the second ball is red?
As usual, .let $B$ be the event second is red, and let $A$ be the event the first is red. We want $\Pr(A|B)$, which is $\Pr(A\cap B)/\Pr(B)$. It should not be hard to compute the two probabilities. It would be very helpful if you indicated what you had tried, so that appropriate help could be given.
2d
comment If $N\equiv 1\pmod 4$ does then follow that $p\equiv q\equiv 1\pmod 4$
@testboy: I do not know a computationally efficient way for very large $N$. Interesting question!
2d
revised How many different values $3a+8b$ can take if $0\leq a\leq 10$ and $0\leq b\leq 21$?
edited body
2d
comment How many different values $3a+8b$ can take if $0\leq a\leq 10$ and $0\leq b\leq 21$?
@Kavya: Our editings crossed paths! As you noticed, I had confused $8$ and $3$, so the count was wrong. But, as you saw, it was fixable.
2d
revised How many different values $3a+8b$ can take if $0\leq a\leq 10$ and $0\leq b\leq 21$?
added 217 characters in body
2d
revised How many different values $3a+8b$ can take if $0\leq a\leq 10$ and $0\leq b\leq 21$?
added 217 characters in body
2d
revised How many different values $3a+8b$ can take if $0\leq a\leq 10$ and $0\leq b\leq 21$?
added 217 characters in body
2d
answered How many different values $3a+8b$ can take if $0\leq a\leq 10$ and $0\leq b\leq 21$?
2d
comment How many ways can one re-arrange the letters in the word QUIBBLE to form a string of 7 letter strings or words, sensible or not?
I would prefer "arrange," since the common sense meaning of "rearrange" is that something moves.
2d
comment Convergence of $\sum_{n=0}^\infty \frac{\sqrt{1+x^n}}{x^n}$ in the case $x<0$ and an analogous problem with $\sum_{n=0}^\infty \frac{x^n}{2+x^n}$
If $x\lt -1$ then after a while we are trying to find the square root of a negative number, no good. At $x=-1$ you can compute, see that we do not have convergence. And for $-1\lt x\lt 0$ it is even worse, the terms blow up in absolute value.
2d
comment Poisson counting process question, but correct answer not obtained by usual method
I would suggest going back to fundamentals, and writing out a solution as follows. Let $A$ be the event no fish in first hour, and let $B$ be the event $2$ fish in $4$ hours. We want $\Pr(A| B)$, which is $\Pr(A\cap B)/\Pr(B)$. The calcuation of $\Pr(B)$ is easy. For $\Pr(A\cap B)$, this is the probability of no fish in first hour times the probability of $2$ fish in the next three hours.
2d
comment Poisson counting process question, but correct answer not obtained by usual method
The probability of the wrong event was computed incorrectly. The first solution multiplies the probability of $2$ fish in $4$ hours by the probability of no fish in the first hour. If the events were independent, which they are not, ths would give us the probability of $2$ fish in $4$ hours and $0$ fish in one hour. But the problem asks us to compute a conditional probability, which is something else entirely.
2d
revised Wilson's Theorem proof
added 34 characters in body
2d
answered Wilson's Theorem proof
2d
reviewed Leave Open What is an Empty set?
2d
reviewed Leave Open Challenging recurrence relation problem
2d
comment How to prove a linear transformation is onto if it is one to one.
If the image of a basis is linearly dependent, that contradicts one to one. For linear dependence means a non-zero vector gets sent to the zero vector, but also the zero vector is also sent to the zero vector. And if the image is linearly independent, the mapping is onto.
2d
comment How to prove a linear transformation is onto if it is one to one.
Consider what it does to a basis.
2d
reviewed Leave Open Notation Question(Abstract Algebra)