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Free expand & simplify calculator - Expand and simplify equations step-by-step.
- Trigonometric Simplification Calculator
simplify\:\tan^4(x)+2\tan^2(x)+1 ;...
- X-5
expand\:(4x^2-3)(3x+1) expand\:(x^2+3y)^3 ; Show More;...
- Foil Method
expand\:(5+x)(8-x) expand\:(x+4)(x^{2}+5)...
- Expand 3
expand\:(2x-5)(3x+6) expand\:(4x^2-3)(3x+1)...
- Roots
roots\:x^{2}+2x+1 ; roots\:2x^{2}+4x-6 ; Show More;...
- 2X-5
expand\:(4x^2-3)(3x+1) expand\:(x^2+3y)^3 ; Show More;...
- 4X^2-3
expand\:(2x-4)(x-5) expand\:(2x-5)(3x+6)...
- Complete The Square
complete\:the\:square\:2x^{2}+6x+2 ;...
- Trigonometric Simplification Calculator
Aleksandar Barišić Barni, scenarista kultnih domaćih filmova kao što su "Crni bombarder", "Kako je propao rokenrol" (druga priča) preminuo je u Beogradu, u 51. godini.
Question. A sequence is defined by the recurrence relation \ ( {U_ {n + 1}} = 3 {U_n}\) and has \ ( {U_0} = 1\). a) Find the first five terms of the sequence. b) Determine the formula for \ (...
May 3, 2014 · The sum of 0 + ⋯ + n − 1 is 1 2(n − 1)n. Here n is the number of users; there are 0 comparisons needed for the first user alone, 1 for the second user (to compare them to the first), 2 for the third user, and so on, up to the n th user who must be compared with the n − 1 previous users.
- Sequence
- Finding Missing Numbers
- Many Rules
- Simplest Rule
- Finding Differences
- Second Differences
- Other Types of Sequences
A Sequenceis a set of things (usually numbers) that are in order. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Seriesfor a more in-depth discussion.
To find a missing number, first find a Rulebehind the Sequence. Sometimes we can just look at the numbers and see a pattern: Did you see how we wrote that rule using "x" and "n" ? We can use a Rule to find any term. For example, the 25th term can be found by "plugging in" 25 wherever nis. x25 = 252= 625 How about another example: Now what does xn-1...
One of the troubles with finding "the next number" in a sequence is that mathematics is so powerful we can find more than one Rule that works. So, we have three perfectly reasonable solutions, and they create totally different sequences. Which is right? They are all right.
When in doubt choose the simplest rulethat makes sense, but also mention that there are other solutions.
Sometimes it helps to find the differencesbetween each pair of numbers ... this can often reveal an underlying pattern. Here is a simple case: The differences are always 2, so we can guess that "2n" is part of the answer. Let us try 2n: The last row shows that we are always wrong by 5, so just add 5 and we are done: Rule: xn= 2n + 5 OK, we could ha...
In the sequence {1, 2, 4, 7, 11, 16, 22, ...}we need to find the differences ... The second differencesin this case are 1. With second differences we multiply by n22 In our case the difference is 1, so let us try just n22: We are close, but seem to be drifting by 0.5, so let us try: n22 − n2 Wrong by 1 now, so let us add 1: We did it! The formula n...
Read Sequences and Seriesto learn about: 1. Arithmetic Sequences 2. Geometric Sequences 3. Fibonacci Sequence 4. Triangular Sequence And there are also: 1. Prime Numbers 2. Factorial Numbers And many more! Visit the On-Line Encyclopedia of Integer Sequencesto be amazed. If there is a special sequence you would like covered here let me know.
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Algebra Calculator shows you the step-by-step solutions! Solves algebra problems and walks you through them.
