pattern

1. Sequences and Series Question (Grade 11)

Determine the value of n for which (2^1)(2^2)(2^3)(2^4)...(2^n) = (2^253) Here's my work so far: 2^1 x 2^2 x 2^3 x 2^4... 2^n = 2^1+2+3+4+...+n, where 1+2+3+..., tn = 253 2^2.2^3 = 2^2+3 = 2^5 = 32 I'm confused on what to do next?
2. Fibonacci Seq bit string proof. Show that pattern can't have three consecutive 1s

I'm having a little trouble figuring out how to prove this. So, the sequence is as follows: S0 = 0 S1 = 1 S(n-2)S(n-1) for all n >= 2 That means S2 = 10 S3 = 101 S4 = 10110 S5 = 10110101 Now the question that I'm stuck on is: Prove that the pattern can't have three consecutive ones...
3. Is there a certain pattern for Kleene closure of a language?

Hi guys. I'm currently studying formal languages for our class. I encountered this example on our study material which I'm not fully understanding: Alphabet = {0,1} K1 = {10,1} K2 = {011,11} K1* = {e, 10, 1, 101, 11, 101010, 10101, 111, 11110, ...} K2* = {e, 011, 11, 011011, 01111, 1111...
4. Pattern or Delusion

We go from natural numbers to integers and gain closure for the operation of subtraction while losing the notion of beginning. We go from integers to rational numbers and gain closure for the operation of division while losing the notion of next. We go from reals to complex numbers and gain...
5. A number pattern problem

Could you please help me with the method to solve the following problem? if the first page of a book contained 1 sticker, the 2nd page 2 and the last page, page 31 contained 31 stickers. How many stickers in the book all together? Thanks
6. Another Pattern Problem

A sequence is given as follows: 1,333,55555,7777777,999999999,................ The 111th term of this sequence will be ? How to find the rule for this sequence ? How to find the nth term ? Please advice! Thanks in advance !
7. What's the pattern rule

We are given the following sequence:- 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,.................. a) What is the 77th element ? b) The sum of the first 100 terms of the sequence is ? c)The sum of the 1st, 2nd, 4th, 7th, 11th, 16th,...........211th terms is ? I was unable to find the rule...
8. Cuboid + ratio/number pattern qn

Hi, I have 2 questions. One to do with geometry and another on number pattern probably. Been having issues with these 2 qns for quite some time..hopefully someone could help Q1) Tina used 1-cm cubes to build a cuboid measuring 40cm by 20cm by 30cm. She rearranged the 1-cm cubes to build 2 large...
9. Diminished Radix Complement (geometric pattern)

So I'm reading about Radix Complements on Wikipedia, and there is a geometric pattern used to prove the following statement: The radix complement is most easily obtained by adding 1 to the diminished radix complement, which is (bn-1)-y. Since bn-1 is the digit b-1 repeated n times because bn-1...
10. How can I find the pattern ?

If we assumed 13 = 24.14445188 16 = 133.0360355 18 = 460.2708264 22 = 6793.53781 36 = 441887042.5 Then find 25=??
11. Solving a pattern regarding modulus

Hi everybody, i'm studying for my discrete math final next week and i'm having an issue with a certain problem. I have to solve this pattern regarding modulus: 5 8 56 45 23 34 67 2 3 3 3 5 4 23 4 5 5 ? ? ? ? (filling in the ?s) N = 3 I'm pretty sure I need to form a certain...
12. Develop Model Emulating Given Wave Pattern

Question: Develop a model for producing a repeating pattern of 8 waves, with 6 smaller waves of approx. the same size and the second and sixth waves much larger. The sketch below gives a general indication of the eight wave pattern. (Sorry for large image) I would like to know how to "take...
13. Finding a pattern within a sequence

For study I need to find 4 patterns within the Lazy Caterer's sequence (1,4,7,16,22,29,37,46,56 etc) and I have no idea where to start. If you can help it would be very very very appreciated :) have a good night,
14. What is the pattern in these numbers

1, 2, 7, 20, 61, 182
15. primes squared inf showing a pattern with the last digits

1. so if i take a prime and square, cube, etc inf times, the last numbers will (so far) be four numbers repeating inf. 2. if i take 5 to the 3rd power and up inf times the last 3 numbers will alternate between 125 and 625. My background in this is type of working numbers is non existent. Up...
16. Write the bit pattern for the decimal value

Assuming a three-bit exponent field and a four-bit significand, write the bit pattern for the following decimal values: (a) -12.5 (b) 13.0 (c) 0.43 (d) 0.1015625 Here are the answers I got for each: (a) 1 110 1010 (b) 1 110 1010 (c) 0 001 1011 (d) 0 000 1101 I don't know how...
17. Help! Work out the pattern of the cards!

I have been presented with this: http://i.imgur.com/wWk6JhW.jpg and been told to work out the pattern of the cards. I am stumped. Anyone have any clues?
18. Line Integral for a sawtooth pattern

I have to evaluate the line integral: \int_Z(sin y + 2x) dx + (2y + x cos y)dy from the point (0,0) to (1,1) to (3,-1) to (4,0). I evaluated the integrals for each of the 3 separate lines such that: \int_Z = \int_{C_1} + \int_{C_2} + \int_{C_3} I got the answer of 2cos(1) - 3sin(1) -7 but I...
19. Finding a pattern to a Summation Series of n^n

Hi there, I stumbled upon a weird question in one of my exams which I couldn't solve so I out of curiosity I wanted to see what the solution could be. Here goes: Given some natural number N and some natural number Z, how would you find out if the following summation is divisible by Z...
20. Colour coded sequence pattern

I'm terrible at maths, but I'm usually OK at generating a formula to feed a calculator or put in code. But for some reason, this has stumped me. I'm not even sure its meant to be in this forum, if not, please move it. I have a colour coded sequence pattern, there are 12 colours, each colour is...