https://padlet.com/lucywon822/pgug53i0wqew Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-16 16:53:32 UTC 2026-02-07 09:33:33 UTC hello@padlet.com lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044431 The domino effect
Math Induction is used to prove both series / sum and divisibility statements.]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044431 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044433 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044433 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044434 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 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044434 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044435 Don't forget to at k+1 to both sides For divisibility t = the leftover from the factor]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044435 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044436 Check your numbers you input and check if you distributed properly]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044436 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044437 - Approximate e^x, trigonometric values, and logarithms of negative numbers by using series. 
- 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.
Know what the Fibonacci series is and why is it important.]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044437 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044438 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044438 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044439 Evaluate the natural log of a negative number as a complex number. e^ia = cosπ + i sin a
1) Substitute π for the angle.
e^iπ = cosπ + i sin π
2) Simplify
e^iπ = -1 + i(0)
e^iπ = -1
3) Take the natural log of both sides]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044439 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044440 On e^x problems, don't round along the way.]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044440 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044441 Utilise the In & e sign in your calculator to solve equations.]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044441 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044443 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044443 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044444 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044444 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044445 Expand a binomial
Find a term in the series]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044445 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044446 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 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044446 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044447 Math -> Probability -> 4 -> ! 
Make sure parenthesis around terms]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044447 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044448 - Sigma is the upper case Greek Letter which in math is used to indicate a sum or series 
- n = 1 is the starting value of n 
- k is the maximum value of n 
- An is the an expression for the general term ]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044448 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044449 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044449 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044450 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 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044450 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044451 Remember that the n value on the bottom of the sign is the starting point ]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044451 lucywon822 https://padlet.com/lucywon822/pgug53i0wqew/wish/352044452 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-16 16:53:32 UTC https://padlet.com/lucywon822/pgug53i0wqew/wish/352044452