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Apr
14
comment Optimization issue, how to obtain the maximal value?
@user143002 I don't have time right now, but will take a look later unless someone else does. One tip: let $B=0$ and try to solve. Then let $B=1$ and try to solve, and so on. You may see a pattern arise !
Apr
14
comment Optimization issue, how to obtain the maximal value?
You could try to simplify first, e.g. since $N$ and $B$ are identified positive integers, then ${N+B\choose B}$ can be replaced by a constant, $\lambda$, say. You may also be able to simplify the sum in the denominator using the Binomial Theorem somehow.
Apr
5
awarded  Necromancer
Mar
29
awarded  Nice Question
Mar
26
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
@GerryMyerson - so we just take logs and apply the usual tools?
Mar
26
accepted Why does this product diverge?
Mar
26
comment Why does this product diverge?
Ok, thanks all I think I've cleared this up now. Basically it all depends on what we mean by an infinite product. Using the standard "sequence of partial products" then we have divergence, but if we explicitly state @Sabyasachi's intention, $$\lim_{n\to\infty}\prod_{k=1}^{2n}a_n,$$ then we have convergence. Delicate!
Mar
26
comment Why does this product diverge?
This is where I misunderstand. The upper index in the product is always $2n$, so by definition the product is never defined with an upper index of $2n+1$. Maybe this is one of those "murky" $\infty$ areas since $\infty$ is not a natural number? ...
Mar
26
asked Why does this product diverge?
Mar
26
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
When $p=1$, taking logarithms gives $\log p=0$ not $\log p=\infty$. Is that a typo?
Mar
26
revised Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
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Mar
25
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
Yes, I thought so. Thanks. Is this still the case if the $a_n$ are monotone decreasing or increasing?
Mar
25
asked Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
Mar
19
revised Find $(a+ib)^{492}$ given that $(a+ib)^{493}=1$
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Mar
13
comment Logarithmic quotient
Given the distinction made, what base logarithm is $\log$ here ? Also - you're missing a bracket second line up from the bottom.
Mar
13
comment Describing the sequence A224239.
Analytic Combinatorics may be of help. Try constructing a class of combinatorial objects you require and then apply a transfer function to obtain a generating function which you can solve explicitly or asymptotically.
Mar
9
comment Help finding value of x in logarithms?
Presumably you $\log$ is base $10$?
Mar
9
comment Help finding value of x in logarithms?
Raise both sides to the power $1/8.4$.
Mar
8
comment Can every definite integral be computed symbolically?
But what about when $b=\infty$...
Mar
4
revised if $f(x) = \int_{t=1}^{t=x^2} t\sin^2(t)\operatorname d\!t$ then $\frac{\operatorname d\!f(x)}{\operatorname d\!x}=?$
added 2 characters in body