https://padlet.com/kienbui2810/v61rz11sp0xb Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-15 17:42:58 UTC 2025-10-01 21:35:21 UTC hello@padlet.com kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351748998 Used to find validity of mathematical statements. Used in three steps. Can be used for both series/sum.]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351748998 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749000 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749000 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749001 Series proof.
Divisibility proof.
Use 3 steps of induction.
Show n=1 works.
Assume n=k works.
Show n=k+1 works.]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749001 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749002 Make sure that, for the first part of step 3, make sure that you add the n=k and n=1 value before you move onto step two and find n=k+1]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749002 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749003 To find divisibility, you can use p = qr, p, q, r]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749003 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749004 Fibonacci Sequence represents many patterns found in nature.
Euler's method for e^x can be estimated through exponential series.
Trigonometric series and Euler's Formula sprout from this exponential series.]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749004 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749005 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749005 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749006 Exponential series: for e^x, find 1 + x + ((x^2)/(2!))
Trigonometric series for cosine: for cos x, find 1 - ((x^2)/(2!)) + ((x^4)/(4!))
Trigonometric series for sine: for sin x, find x - ((x^3)/(3!)) + ((x^5)/(5!))
Euler's Formula: e^(ia) = cos a + i sin a
Remember that ln(-1) = i*pi]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749006 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749007 On e^x problems, don't round along the way.]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749007 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749008 For Factorial (!): Press Math, then go to the PRB column, press 4, then press enter]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749008 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749009 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749009 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749010 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749010 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749011 Use Pascal's triangle to expand each binomial.
Find the (fifth) terms of (4a + 3b)^7

]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749011 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749012 When the title says Find the fourth or fifth term of a binomial, the result of "r" will always be the lesser amount of the term by 1. ]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749012 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749014 Binomial theorem formula:
plug in certain values for exponents
put in correct order of the fraction (use parentheses).]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749014 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749017 Uppercase Greek Letter Sigma. Used to find sum/sequence of multiple terms in an equation.]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749017 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749018 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749018 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749019 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.]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749019 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749020 When the sigma is infinity, we need to use formula S=a1/(1-r) to find the sum. Can not solve with calculator.]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749020 kienbui2810 https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749021 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-15 17:42:58 UTC https://padlet.com/kienbui2810/v61rz11sp0xb/wish/351749021