# sequence

1. ### Sequence with variable pattern

Hello. I've got the sequence below and I wonder if it has a public formula or not. 1 , 2 , 4 , 7 , 11 , .... The pattern is actually growing by one each step. 1 +1 =2 2+2 = 4 4+3=7 7+4=11 11+5=16 . . . I didn't know which thread to post it by the way . thank you.
2. ### Limit,sequence

Evaluate L=\lim_{n\rightarrow \infty} \dfrac{n^{n^2 +n +1}}{{e^{n^2 }(1^1 \cdot 2^2 \cdot \dotsc \cdot n^n ) }}.
3. ### A limit with factorials

Evaluate \lim_{n\rightarrow \infty }n!^{-n!}\cdot n^{n^{n}} .
4. ### Probability with sequence

Given sequence s:\{ n, 1+n, 2+n, 3+n, ...., 2n \} , find probability such that when we choose n random elements from the sequence , their product is minimal.
5. ### Geometric sequence

How can I find x so that a+x, b+x, c+x is a geometric sequence?
6. ### (!MUST READ!) So, I found this odd sequence...

I was fiddling around with some square numbers two days ago, when I started doing this (finding differences): 0,1,4,9,16,25,36,49,64,81,100,121,144,169 1,3,5,7, 9 ,11,13, and you see where this is going. All the numbers in this row are odd numbers, two different. What about cubed... 0...
7. ### arithmetic sequence

Question (given): A pharmacy sees that its sales of cold medications increase steadily from the beginning of May. Their sales record shows that last year they sold 26 packets of cold tablets in the first week in May. The sale of cold tablets increased by seven packets each week. 1. on the...
8. ### A sequence..

Any ideas on how to generate this sequence? $$S = 1,3,7,14,27,46,75,115,169,234,315,415,537,673,839,1033,1261,1520,1809,2138,...$$ First few terms follow some variant of Sterns sequence but doubt it means anything. Also the original sequence is $S' = 4 S$..
9. ### Limit with sequence

Simple Limit Evaluate \lim_{x\rightarrow 2 } \frac{2^x - x^2 }{2x-\sqrt{8x}}.
10. ### Help : Deriving an inequality related to Lucas Sequence

Hi, I am studying a paper by Yann Bugeaud (click here), on page 13 there is an inequality (16) as given below- $\Lambda:=\left|\left(\frac{\alpha(\gamma-\delta)}{\gamma(\alpha-\beta)}\right)\left(\frac{\gamma^{s}}{\alpha^{r}}\right)^{-d}-1\right| \ll \alpha^{-\eta r d}$ which is obtained from...
11. ### Symmetries when expanding Thue Morse sequence in layers of rings

By generating Thue Morses sequence in rings and study the natural numbers N (including 0) represented by radial binary combinations some geometrical properties emerges, such as: * All odd integers will be arranged in a specific geometric order * Even integers will be arranged in a specific...
12. ### How to get to this sequence?

If d1=s*(1-a) and d2=s*(1-a)+(1-s)*(1-a)*s and d3=s*(1-a)+(1-s)*(1-a)*s+(1-s)*(1-a)*s how is it that the total d after n times is d=[1-(1-s)^n] *(1-a)^n ?
13. ### Limit with sequence

Evaluate \lim_{n\rightarrow \infty} \frac{(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n})^n }{n}. To write it in short-terms : \lim_{n\rightarrow \infty}n^{-1}H_{n}^{n} \; , H is the harmonic series .
14. ### Can an infinite sequence be missing one of such sequences?

Can an infinite sequence of finite sequences of combinations of a finite number of elements be missing one of such finite sequences? (If the rules do not prohibit such a finite sequence.)
15. ### Limit with sequence

Evaluate \lim_{n\rightarrow \infty}\frac{1^1 \cdot 2^2 \cdot 3^3 \cdot ... \cdot n^n }{n^{n^2 }}\; \; , n\in \mathbb{N}. To write it different : \lim_{n\rightarrow \infty } n^{-n^2 } \prod_{k=1}^{n} k^{k} .
16. ### Multivariable calculus - Limits

Show that the function f(x,y)=y/(x-y) for xâ†’0, yâ†’0, can take any limit. Construct the sequences { f(xn, yn } with (xn,yn)â†’(0, 0) in such way that the lim nâ†’âˆž f(xn,yn) is 3,2,1,0,âˆ’2. Hint: yn=kxn. I am not sure whether I am right, but I did the following: f(x,y) = kxn/(xnâˆ’kxn) =...
17. ### Reverse Geometric Series computer program.

Reference : Geometric Progression - Series and Sums - An introduction to solving common geometric series problems. Can we write a Computer program which will print Reverse Geometric number series? Output of the program will be 243,81,27,9,3,1 Can we start from 81 till 1 for the program...
18. ### Limit with sequence

How can I solve the limit or which theorem can be used ? \lim_{n\rightarrow \infty } \frac{1^n +2^n + 3^n +...+n^n }{(n!)^2} .
19. ### Sequence&Series

Given the exponential sequence 3, 9/2, 27/4, ..., find the number of terms for its sum to be greater than 368.
20. ### Simple sequence

Find n-th term or function f(n) that defines the sequence 2,2,0,0,0,....\; \; (infinite zeros after second term)