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App developer, Research Associate, and Lecturer of and dabbler in Mathematics.


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 $1$
added 82 characters in body
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 $(a+ib)^{493}=1$
added 5 characters in body
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
Mar
4
suggested suggested edit on Is the intersection empty?
Feb
28
accepted Solution of “quadratic equation” involving functional coefficients.
Feb
27
revised Solution of “quadratic equation” involving functional coefficients.
added 12 characters in body
Feb
27
revised Solution of “quadratic equation” involving functional coefficients.
edited body
Feb
27
asked Solution of “quadratic equation” involving functional coefficients.