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 2 years ago
Think of 3 rules, such that they generate 2,3,6 as the first 3 terms of a sequence.
 2 years ago
Think of 3 rules, such that they generate 2,3,6 as the first 3 terms of a sequence.

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amistre64
 2 years ago
Best ResponseYou've already chosen the best response.31/2 3/2 4 i came up with this one:\[\frac{1}{2}\left(\frac{n1.5}{n1.5}+\frac{3n7.5}{n2.5}\frac{8n280}{n3.5}\right)\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3lol, i forgot to delete my reference scribbles

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3i was also considering coming up with something such that:\[\int_{0}^{n}f(x)dx=2,3,6~for~n=1,2,3\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3the first one i thought of was\[a_n=n^22n+3\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1346159138909:dw hmm; such that the first area is 2, and the second is 1, and the third is 3

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3if i could determine the slopes in that figure, i could integrate the function to get what im thinking of :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1346159507196:dwba=1\[\int_{a}^{b}k~dx=F(b)F(a)=1\]F(b)=4, F(a)=3

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1346159801695:dw 0 to b , b<1 ... its like right on the tip of my brain

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1346160036988:dw at a, A=2, at (ba)/2, A=0 so there has to be a sweet spot between a and the midpoint that satisfies my quandry

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3if b= 3/4; and a = 1/4 \[\frac{4}{3/4}x=\frac{16}{3}x; \int\to\ \frac83 \left((\frac34)^2(\frac14)^2\right)\]\[\frac83 \left(\frac{91}{16}\right)=1\frac13\] so its between 1/4 and 1/2 :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1346161272353:dw hmmm

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3not B=8, 4+4=8/2=4; that triangle area there is B=4

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3if i guess that: (4+d)/2 = 3; d=2 mxd 4+2 = 6, 6 in 1 = 6x, 6x2 3x^22x, (0,1) = 32=1

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1346162349632:dw

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.32,3,6 is my goal; and i wonder if alternating signs, and doubling would give me my needed slopes, making the next one 12 12x2; 6x^22x = 4, not 3 it was a nice guess

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3int mx2 , [0,1] m/2  2 = 3 m/2 = 5 m=10

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1346163082261:dw

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3abc = 4 abc=6 a+bc=10 rref{{1,1,1,4},{1,1,1,6},{1,1,1,10}} 5,8,7 f(x) = 5x1+8x27x3 and since n=0 = 10; lets add 10 to it to move it to the proper spot \[\int_{0}^{n}f(x) = 5x1+8x27x3+10~dx=\{2,3,6,...\}~:~n=1,2,3,...\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3\[\int_{0}^{n}f(x)~dx\]\[\int_{0}^{n} (5x1+8x27x3+10)~dx=\{2,3,6,...\}~:~n=1,2,3,...\] that fixes the typos

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3ima goofy goober!!! lol

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3i know right, i should be soo ashamed

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0i guess my idea of a second degree polynomial is too prosaic. you probably did that first anyway

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0maybe change it to "find the most arcane sequences whose first three terms are ..."

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3i did .... and my second original idea was:\[a_{n+1}=a{n}*a_{n1}~:~a_1=2, a_2=3\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3if by arcane you mean deviously clever ... i agree

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0i really meant "off the wall" not arcane

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3i wonder what the math teachers gonna give me as a grade on the homework this year; or if shell even read it

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0you will get a gold star for cleverness

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3i gotta hobble over to physics and 2 other classes for awhile; yall try not to break stuff while im gone

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large{s_n=2n\frac n4\left(1+(1)^n\right)}\] \[s_1=2\frac 14\left(1+(1)^1\right)=20=2\] \[s_2=2\times2\frac 24\left(1+(1)^2\right)=4\frac12(2)=3\] \[s_3=2\times3\frac 34\left(1+(1)^3\right)=60=6\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0\[a_n=(1)^{n}n^2\cos(\pi n)+(1)^{n+1}2\cos(\pi n)+(1)^n3\cos(\pi n)\]

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0Why is interesting? I do not know. Here is my simple contribution. \[ a_1=2\\ a_2=3\\ a_n=a_{n1}a_{n2},\quad n>2 \] \[ a_1=2\\ a_2=3\\ a_n=a_{n1}+a_{n2}+1,\quad n>2 \] \[ a_1=2\\ a_2=3\\ a_n=a_{n1}a_{n2}+5,\quad n>2 \]

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0Here are two more. You can have infinite such rules. \[ a_1=2\\ a_2=3\\ a_n=2 a_{n1} ,\quad n>2 \] \[ a_1=2\\ a_2=3\\ a_n=3 a_{n2} ,\quad n>2 \]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3the question was so bland that i figured id see if there were more interesting ways to develop a sequence that began with the given digits.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3if my teacher insists that i have to do the homework for a grade .... im at least going to try to get some fun out of it :)

Herp_Derp
 2 years ago
Best ResponseYou've already chosen the best response.1\[a_n=\Pi (n)\Gamma (n) +2\] \(\Pi (n)=n!\) and \(\Gamma (n) =(n1)!\) but it just looks so much cooler that way.

Herp_Derp
 2 years ago
Best ResponseYou've already chosen the best response.1This one is just... idk \[\large a_n=\left\lfloor\sqrt[n]{n+\Big\lfloor e^{\frac{1}{2}n^2}\Big\rfloor}\right\rfloor +\left\lfloor\int_0^n \frac{\frac{1}{2}xe^{\sqrt{x}}}{\sin (x)}\,\text{d}x\right\rfloor\]
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