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3h
comment If the average of 2 successive years’ production 1/2($a_n + a_{n-1}$) is 2n + 5 and $a_0=3$, find $a_n$.
I would write $b_n=a_n+cn+d$, substitute in, and find $c,d$ to give $b_n=-b_{n-1}$
4h
comment If the average of 2 successive years’ production 1/2($a_n + a_{n-1}$) is 2n + 5 and $a_0=3$, find $a_n$.
If you don't have any better ideas, a reasonable next step is to calculate some values. A spreadsheet makes this easy with copy down. In this case it jumps out that $a_{4k-3}=a_{4k}=8k+3$ with $a_{4k-2}=8k-1, a_{4k-1}=8k=7$ That becomes a target for induction.
8h
comment Do complete graphs maximize the number of triangles?
Bingo. Thanks......
8h
answered If $a_{2n}$ and $a_{3n}$ converges does $\lim(a_{2n}) = \lim(a_{3n})$
8h
comment Do complete graphs maximize the number of triangles?
There should be a button at the bottom of your question marked "edit". You could put the correction in. At the same time, you could click the link icon at the top and make the linked question title into a link. Thanks. I could do the first, but don't have the link.
8h
comment Prove that one of x,y,z is smaller than 3 and one is bigger than 5 if…
For the first, I made $z$ just a little bigger than $3$, and we said $y \ge z$, then got $x$ from the sum being $2$. Similarly for the second, I made $x$ a little below $5$, then we said $y \le x$, then got $z$ from the sum.
8h
comment Prove that one of x,y,z is smaller than 3 and one is bigger than 5 if…
I have fixed the first part.
8h
revised Prove that one of x,y,z is smaller than 3 and one is bigger than 5 if…
correct
8h
answered Calculating the probability of receiving all possible rewards after 15 events
9h
answered Prove that one of x,y,z is smaller than 3 and one is bigger than 5 if…
9h
answered The coupon collectors problem
1d
answered Help with Runge-Kutta method for solving systems of differential equations
1d
comment Four Isosceles Trapezoids
Yes, because they are then either both integers or both half integers. If they are half integers, A will not be an integer.
1d
comment Four Isosceles Trapezoids
I the fisrst paragraph you mean "trapezoids" not "triangles" twice
1d
comment how likely is it that 2 strangers in a city of 8 million will cross paths?
You have to define what you mean by "lives overlap" and "parallel lives affect each other" precisely enough that you can calculate the chance that a given pair of people will do that. That part is not mathematical. Having done so, math can help you with how this scales to a city population.
1d
answered Finding the points of a paramertized curve where a tangent line has slope 3?
1d
answered Prove that $ 2^n \not \equiv 1 \pmod{n} $ for any $n > 1$.
1d
comment Prove that $ 2^n \not \equiv 1 \pmod{n} $ for any $n > 1$.
"For any" is an English term that is not well defined in mathematics in the presence of a negation. Your sentence can be read as "2^n \equiv 1 \mod{n} is false for all $n \gt 1$" or as "2^n \equiv 1 \mod{n} is false for some $n \gt 1$. If the statement were positive it would clearly be "for all $n \gt 1$
2d
comment Numeric methods?
@Bak1139: Adding a non continuous function to a continuous function results in a non continuous function. But it is possible to add two non continuous functions and get a continuous one.
2d
comment progressive dinner
No, try filling in a table and you'll get stuck early. For $16$ couples there are $\frac12\cdot 16 \cdot 15=120$ pairs. If you have six couples to a course, you cover $15$ per course, so you might be able to do it with eight courses.