# sequences

2. ### Limits with sequences

Evaluate: a. l=\lim_{N\rightarrow \infty } \underbrace{sinsin...sin}_{N}N. b. l=\lim_{n\rightarrow \infty } n!^{-2n}\prod_{i=1}^{n}i^i . c. l=\lim_{n\rightarrow \infty } \frac{\sum_{i=1}^{n^2 }i^{-1}}{\ln(n)}.
3. ### T Sequences - Explicit Enumeration of $\epsilon_0$

Introduction: Making a Sequence $T$ based on â€œThe Rule of Threeâ€ The goal of this thread is to develop the basic model for what I refer to as a "$T$ sequence" and then expand on the basic model so as to create an enumeration of the ordinal $\epsilon_0$. Each $T$ sequence is a listing of...
4. ### Word Problem Sequences and Series

A Mining Company was founded in 1894 and the mineâ€™s initial production was the extraction of 100kg/year of silver. Each following year saw a steady increase of 60kg/year until the silver production peaked at 700 kg/year. Production remained at this level until 1914, when an event caused the...
5. ### Greatest Common Divisor of two specified sequences of numbers (search for equality)

I consider two sequences of numbers $A=\{a_1,...,a_n\}$ and $B=\{k-a_1,...,k-a_n\}$, where $a_1 \le a_2 \le ... \le a_n \le k$. I am looking for such conditions under which: $gcd(a_1,...,a_n) = gcd(k-a_1,...,k-a_n)=1$. In more general form: $gcd(a_1,...,a_n) = gcd(k-a_1,...,k-a_n) \ge 1$...
6. ### 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.)
7. ### An infinite set of finite sequences of combinations of a finite set of elements

An infinite set of finite sequences of combinations of a finite set of elements is an infinite uncountable set?
8. ### Book about Summation and Product of Sequences

Hello, I would like to know if there is any book devoted to summations and product of sequences (pi notation). With theory and good exercises.
9. ### Mathematical series & sequences computer programs for printin series in reverse order

Reference: https://www.google.com/amp/s/edublognss.wordpress.com/2013/04/16/famous-mathematical-sequences-and-series/amp/ Can we write computer programs for the mathematical series & sequences link given above which will print the series in reverse order? Programming languages could be...

How do you find the nth term (edit) which have say the fifth term ascending instead of descending e.g. -576; -1025, -1728, -2816, -2241
11. ### 1/998001 goes way deeper than expected

Is the above post needed now, given your later post on the same matters?
12. ### 1/9801 and even deeper examples

These reciprocals are nothing new, but are surprising and link into other areas of maths and many types of sequence. I've seen the terms generators and generating sequences used with these, but haven't seen more than the simplest examples elsewhere. 1/9801 = 00010203â€¦ 1/998001 =...
13. ### Can you solve these sequences?

Hi Can you solve these? 1) 12345, 21295, 218143, 2812793, ? 2) 110, 108, 99, 81, ? Best regards. :D:D
14. ### Geometric sequences

https://www.dropbox.com/s/s944t19skpf47d7/1.jpeg?dl=0 Hello everyone, I've attached the question in the link above. I've done part a,b,c but I'm struggling to solve part d. For part d, this is how I tried to solve it: I rearranged the equation from part c: 1/2(a5*b5)=(b6)(a6)...
15. ### Sequences Discrete Math

Answer requires justification, how would you do this?
16. ### help with limits of sequences

Hello I really troubled with the following questions u_n = \left(\frac{2n^3 - 4n^2 + 5}{10n^3 + 100}\right)\cdot2^{-n} w_n = \left(\frac{3n + 2}{4n^2 + 8n + 5}\right)\cdot\left(\frac{(1 - n)^3}{(14 - 5n)^2}\right) e_n = \frac{2^n + 3^{n - 1} + 5^{2n + 2}}{4^{n - 7} + 5^{2n}} b_n =...
17. ### Limits of Sequences

Hello guys! Really need help with this problem. (I'm sorry, can't upload this photo)
18. ### Limits of Sequences

Hello guys! Really need your help for this problem.
19. ### Geometric Series Problem

I have a math problem I cannot solve and don't have access to a teacher! Can someone help me? The sum of three consecutive terms of a geometric sequence is 24 and the sum of the next three terms is also 24. Find the sum of the first 12 terms. It may be super easy and I just haven't...
20. ### Sequences and Series

Hey! I need help with this question.. An arithmetic sequence has the first term -4 and common difference 1. A geometric sequence has the first term 8 and common difference 0.5. After how many terms would the sum of the arithmetic sequence exceed the sum of the geometric sequence? Thanks!