https://padlet.com/anthony_j_travieso/ud08qbhr8ewd Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-16 16:53:01 UTC 2023-08-07 01:28:35 UTC hello@padlet.com anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044203 The domino effect
Math Induction is used to prove both series/sum and divisibility statements.]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044203 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044204 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044204 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044205 Series proof.
Divisibility proof.
Use 3 steps of induction.
Show n=1 works.
Assume n=k works.
Show n=k+1 works.]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044205 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044206 Don't forget to at k+1 to both sides
For Divisibility t=the the leftover from the factor]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044206 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044207 Check your numbers you input and check the you distributed properly.]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044207 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044208 Fibonacci sequence
Golden Ratio: 1.618
"e"
Euler's Formula]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044208 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044209 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044209 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044210 Finding the value
Using the first few terms and finding there value
Write complex numbers in exponential form
e^x= x^n/n!= 1+x+x^2/2

]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044210 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044212 On e^x problems, don't round along the way.]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044212 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044213 Ln & e^x can be useful to solve these problems.
ln(-1)=i(pi)
ln(e^n)=n]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044213 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044214 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044214 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044215 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044215 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044217 Expand a binomial 
Find a term in the series

]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044217 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044218 When expanding the equation, we need to be cautious of the exponent of the original equation, also with the positive/negative signs.]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044218 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044219 Math -> Probabilty -> 4 -> !
Make sure parenthesis around terms]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044219 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044220 Often mathematical formulae require the addition of many variables Summation or sigma notation is a convenient and simple form of shorthand used to give a concise expression for a sum of the values of a variable.]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044220 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044221 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044221 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044222 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 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044222 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044224 We need to be cautious of the limits of the sigma notation. It can either be a small integer or it can also be infinite.]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044224 anthony_j_travieso https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044225 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-16 16:53:01 UTC https://padlet.com/anthony_j_travieso/ud08qbhr8ewd/wish/352044225