https://padlet.com/hkworld105/nkcbat9odbr0 Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-15 17:21:08 UTC 2024-08-30 09:22:53 UTC hello@padlet.com hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739966 Some equations need to be proven to be an accurate equation representing a sequence. Induction is a way of proving.]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739966 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739967 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739967 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739968 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 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739968 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739971 Make sure you plug in the right numbers or variables.]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739971 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739972 there is no calculator tips for this one, except plugging numbers. 
Equations and other formulas that are included.]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739972 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739974 use Euler's formula to write the exponential form of a complex number. 
Write the natural logarithm of a negative number as a complex number

]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739974 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739975 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739975 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739976 derived by replacing e^x with e^ia
i is the imaginary unit
a is the measure of an angle in radians 
think back to Chapter 9

]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739976 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739978 On e^x problems, don't round along the way.]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739978 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739979 there are many equations that you dont need to calculate 
such as, a+bi = r(cos 0 + isin 0)

r(cos 0 + isin 0) is called the polar form
rei0 is called exponential form of a complex number

]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739979 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739981 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739981 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739982 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739982 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739983 1 type of problem — expand (3x+4y)^3
Use the third row: 1, 3, 3, 1]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739983 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739984 It is better to write every step down because expanding a binomial is a very complicated process.]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739984 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739985 Don’t just plug it in; solve it on paper.]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739985 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739986 Learn what sigma notation is and how to use it
Write a series in sigma notation
Go from sigma notation to an expansion of terms and find the sum

]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739986 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739987 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739987 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739989 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 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739989 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739991 do the calculations correctly
make sure to know the differences n+1 or 1^n]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739991 hkworld105 https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739992 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-15 17:21:08 UTC https://padlet.com/hkworld105/nkcbat9odbr0/wish/351739992