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Apr
15
answered Edited-How can I solve polynomial recurrences like $f(n+1)=\frac{2f(n)}{f(n)+1}$
Apr
15
answered Find the MacLaurin Series for $f(x)=\ln(√81-x^2)$
Apr
15
comment Sine Sum : Inverse Circular Function Proof
@SanchayanDutta, Related : math.stackexchange.com/questions/672575/…
Apr
14
answered If the equation $|x^2+4x+3|-mx+2m=0$ has exactly three solutions then find value of m.
Apr
14
answered using Fermat's little Theorem to find the least residue of $5^{38}\ mod\ 13$
Apr
13
answered simplifiying an expression $(n + 1)! − 1 + (n + 1) \cdot (n + 1)!$
Apr
13
answered Find triangle angle knowing side length change and angle change
Apr
13
answered how to solve $\sin\theta+\sqrt{3}\cos\theta=-\sqrt{3}\;$ for $\;\theta\;$ when $\;0^\circ\leq\theta<360^\circ$
Apr
13
answered how to solve $\sin\theta+\sqrt{3}\cos\theta=-\sqrt{3}\;$ for $\;\theta\;$ when $\;0^\circ\leq\theta<360^\circ$
Apr
13
answered If the positive numbers x,y,z are in harmonic progression, then log(x+z) + log(x-2y+z) equals
Apr
12
answered Basic question about integrating by parts
Apr
12
answered Determine whether the series $\sum_n \frac{1}{n^n}$ converges or not?
Apr
12
comment Find the radius of convergence of the Maclaurin series $x\cdot ln\left(x^2+\sqrt{x^4+9}\right)$
$$(x^4+9)^{\dfrac12}=9^{\dfrac12}\left(1+\dfrac{x^4}9\right)^{\dfrac12}$$ See en.wikipedia.org/wiki/Binomial_series#Convergence
Apr
12
answered Show that $2^{105} + 3^{105}$ is divisible by $7$
Apr
12
comment Solving an equation with the sum of inverse cosine and inverse tangent
@ClaudeLeibovici, How can be there be an infinite number of solutions?According to my answer, there are exactly two solutions, $x=\tan\dfrac\pi{12},\tan\dfrac\pi3$
Apr
12
comment What is the next perfect square of the form 14444… in decimal notation?
$$(10m\pm2)^2=100m^2\pm40m+4$$ We need $100m^2\pm40m+4=\dfrac{13(10^n-1)}9+1$ $$900m^2\pm360m+40=10^n$$ $$90m^2\pm36m+4=13\cdot10^{n-1}$$
Apr
12
revised Limit w/o L'hopital
added 65 characters in body
Apr
12
answered Limit w/o L'hopital
Apr
12
comment Solving an equation with the sum of inverse cosine and inverse tangent
@ClaudeLeibovici, You are right? But, is that the only solution?
Apr
12
answered Solving an equation with the sum of inverse cosine and inverse tangent