https://padlet.com/csrceciliacsr/1ok5js8pbbce Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-16 16:52:26 UTC 2026-01-21 12:45:37 UTC hello@padlet.com csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043903 1) use mathematical induction to prove the validity of mathematical statements.
2) used for both series/sum and divisibility statements.]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043903 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043905 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043905 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043910 Finding Fibonacci from formula
Know what the Fibonacci series is and why it is important.

]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043910 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043911 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043911 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043912 Approximate e^x, trigonometric values, and logarithms of negative numbers by using series.
Rule: Xn=Xn-1 + Xn-2
Xn=term number
Xn-1=the previous term
Xn-2=the term before that

Exponential series: e^x=1+x+(x^2/2!)+(x^3/3!)...
Trigonometric series: cosx=1-(x^2/2!)+(x^4/4!)-(x^6/6!)...
sinx=x-(x^3/3!)+(x^5/5!)-(x^7/7!)...]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043912 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043913 On e^x problems, don't round along the way.]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043913 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043914 most of time calculate first three terms of series. 
1 and x also include as first term.]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043914 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043916 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043916 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043917 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043917 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043918 1) Expand binomials using the Pascal's triangle.
2) Expand binomials using the Binomial Theorem.
3) Find a particular term of a binomial using the sigma form of the Binomial Theorem.

]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043918 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043919 Be aware that n is one less than the term that we are calculating for in the Binomial Theorem.]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043919 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043920 while doing the pascal triangle questions, draw the model on the side first.]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043920 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043921 Mathematicians use Sigma Notation to represent the sum of a series]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043921 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043922 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043922 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043923 Expand a series from sigma notation (plug in the first n value to the formula and keep increasing by 1).
Find a finite sum using calculator.
Find an infinite sum using formula  S=a1/(1-r)
Go from a series to the sigma notation.]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043923 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043925 Be careful about the start point of the series. ]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043925 csrceciliacsr https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043926 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-16 16:52:26 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352043926 aashley_pufo_debate https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352047314 1) Series Proof
- show n=1
- assume n=k works
- show n=k+1 works
2) Divisibility Proof
- show n=1
- n=k
- n=k+1]]> 2019-04-16 17:00:36 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352047314 aashley_pufo_debate https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352048639 1) no basis step
2) wrong induction step]]> 2019-04-16 17:03:57 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352048639 aashley_pufo_debate https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352049182 1) calculator is not required
2) calculations include: foiling]]> 2019-04-16 17:05:22 UTC https://padlet.com/csrceciliacsr/1ok5js8pbbce/wish/352049182