Benjamin Dickman
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 9h awarded Self-Learner Apr 17 comment Convergence of the sequence $x_1 = 1$ and $x_{n+1} = 4 - \frac{1}{x_n}$ for all $n \geq 1$. @user21820 Yes: I believe this observation should simply be pointed to in justifying the final choice of root to which the sequence converges. (I think it is also quite possible that "disregard the negative answer" was intended to mean "disregard the answer with a subtraction sign.") The OP asks about correctness of the proof; I think this last bit of clarity would be helpful. Apr 17 answered Convergence of the sequence $x_1 = 1$ and $x_{n+1} = 4 - \frac{1}{x_n}$ for all $n \geq 1$. Apr 14 revised Prove Using Induction: $\sum_{k=1}^{n} 1/k(k+1) = n/(n+1)$ added 261 characters in body; edited title Apr 6 answered How to derive the formula for the sum of the first $n$ odd numbers: $n^2=\sum_{k=1}^n(2k-1).$ Apr 3 accepted How many $a$-nary sequences of length $b$ never have $c$ consecutive occurrences of a digit? Apr 3 comment How many $a$-nary sequences of length $b$ never have $c$ consecutive occurrences of a digit? Awesome. Is there a straightforward way to extract the coefficients? Apr 3 comment The number of words of length $n$ from specific alphabet with rule of creating. +1. Do you happen to know if a similar approach could work here? Mar 25 comment Why does the limit of this function not exist: $\lim_{x\to \infty} \frac{1}{1+\cos(x)}$ @immibis No, I quite deliberately wrote sequence rather than function. Mar 24 revised Let \$p