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11h
awarded  Nice Answer
11h
answered Is the sum of a unimodal and increasing function still unimodal?
12h
comment Limit of $\{a_n\}$, where $a_{n+1} = \sqrt{2+a_n}$
I hear ISIS is in contact.
12h
comment Limit of $\{a_n\}$, where $a_{n+1} = \sqrt{2+a_n}$
Nested square roots have some interesting and surprising properties. Do a search. Here is one result: en.wikipedia.org/wiki/Nested_radical
13h
comment Limit of $\{a_n\}$, where $a_{n+1} = \sqrt{2+a_n}$
$a_1 = \sqrt{2}$, $a_2 = \sqrt{2+\sqrt{2}}$, $a_3 = \sqrt{2+ \sqrt{2+\sqrt{2}}}$, $a_4 = \sqrt{2+ \sqrt{2+ \sqrt{2+\sqrt{2}}}}$.
13h
answered Limit of $\{a_n\}$, where $a_{n+1} = \sqrt{2+a_n}$
18h
answered Perfect powers of successive naturals: Can you always reach a constant difference?
1d
comment Prove a sequence converges using sub-sequences
I think you would want to use $a^2-b^2 = (a-b)(a+b)$ and $a^3-b^3 =(a-b)(a^2+ab+b^2)$.
1d
comment Find the general values of $x$ satisfying the trigonometric equation
As I just found out.
1d
answered Find the general values of $x$ satisfying the trigonometric equation
1d
comment Split Factorial of n
Got a feeling this is equivalent to a NP problem and, therefore, hard. For a heuristic, sort the integers and start pairing at the ends and from the middle.
1d
answered Trigonometry equation maximum
1d
comment How to find $I=\int_{-4}^4\int_{-3}^3 \int_{-2}^2 \int_{-1}^1 \frac{x_1-x_2+x_3{-}x_4}{x_1+x_2+x_3+x_4} \, dx_1 \, dx_2 \, dx_3 \, dx_4$
Ah, but take that sand, add water, and it turns into mud. Form that mud into blocks, let it dry in the sun, and it turns into bricks which can then be used to construct a magnificent building.
1d
answered How to solve the system of equations $\{10^{-4}x_1+x_2=1, x_1+x_2=2\}$ using finite precision arithmetic with three significant figures?
1d
comment prove function is well-defined and integrable
$\sum x/n^2 = x\pi^2/6$.
1d
comment How to find $I=\int_{-4}^4\int_{-3}^3 \int_{-2}^2 \int_{-1}^1 \frac{x_1-x_2+x_3{-}x_4}{x_1+x_2+x_3+x_4} \, dx_1 \, dx_2 \, dx_3 \, dx_4$
I never worry about convergence until a singularity hits me on the head.
1d
answered Show $\lim_{m \rightarrow \infty} \frac{1}{m^2+1} = 0$ using the $\varepsilon$-$N$ definition of convergence
1d
answered Constructing Polynomial Function from Set of Points and Slopes
1d
comment prove function is well-defined and integrable
The terms of $nx/n^2$ don't make sense, since they simplify to $x/n$ which makes the series $x(1+1/2+1/3+...)$ which diverges.
1d
answered convergence radius and sum of a series