Let $\{f_n(x)\}$ be a sequence of polynomials defined as $f_1(x) = (x - 2)^2$, $f_{n+1}(x) = (f_n(x) - 2)^2$; $n \ge 1$.
139190
What are the coefficients of the polynomial inductively defined as $f_1=(x-2)^2\,\,\,;\,\,\,f_{n+1}=(f_n-2)^2$?
65619
Does $f^{(n)} = 0$ imply that complex $f$ is a polynomial?
155995
Fibonacci proof question: $f_{n+1}f_{n-1}-f_n^2=(-1)^n$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
25532
Determine if the convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ is uniform.
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
91528
sequence $x_{n+1}=x_n+e^{-2018x_n}$
22077
Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
27217
For the Fibonacci sequence prove that $\sum_{i=1}^n F_i= F_{n+2} - 1$
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
156034
sufficient condition for a polynomial to have roots in $[0,1]$
70561
limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
107133
Let f(x) be a polynomial satisfying $\lim_{x \to\infty} \frac{x^4f(x)}{x^8+1}=3,$ $f(2)=5 $ and $f(3)=10$, $f(-1)=2$ and $f(-6)=37$
37906
Prove $s_n$ is a Cauchy sequence for $|s_{n+1}-s_n|\lt2^{-n}$
105882
Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$