https://padlet.com/jakoyamatsu/lcsxe8z3tj8g Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-15 17:32:43 UTC 2023-03-01 14:30:16 UTC hello@padlet.com jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744969 Use mathematical induction to prove the validity of mathematical statements. 
Use it for a series/sum and divisibility statements. ]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744969 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744991 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744991 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744993 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 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744993 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744994 Do not skip over the n=k step.
When beginning the third step, just bring down the term on the right side (do not add k+1 yet). ]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744994 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744996 Use parentheses
Make sure it is in the correct mode. ]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351744996 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745000 Approximate e^x, trigonometric values, and logarithms of negative numbers using series
Use Euler's Formula
Write natural logarithm of negative number
Fibonacci Series and why it's important]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745000 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745003 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745003 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745005 Write a complex number (use Euler's formula)
Approximate the value of e^n (use the first five terms of the exponential or trigonometric series)]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745005 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745007 On e^x problems, don't round along the way.]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745007 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745009 You cannot evaluate a natural log of a negative number as a complex number on a calculator. You have to use Euler's Formula. ]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745009 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745012 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745012 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745015 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745015 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745017 Expand a binomial equation (use Paschal's triangle's numbers. The x will start with the original exponent and descend until zero. The y will start with zero and ascend until the original exponent).
Find a specific term of a binomial (n!/r!(n-r)! x^n-r y^r]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745017 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745019 Remember that n=the original exponent and that r= one less than the term number when using the theorem.]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745019 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745024 Get sigma on the calculator for finite sums: Math button, then Zero. 
Don't forget parentheses! ]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745024 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745026 What sigma notation is and how to use it
Writing series in sigma notation
Go from sigma notation to expansion of terms
Find the sum]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745026 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745027 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745027 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745029 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 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745029 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745030 Only use S=a1/(1-r) for an infinite sum, not a finite sum. ]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745030 jakoyamatsu https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745031 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-15 17:32:43 UTC https://padlet.com/jakoyamatsu/lcsxe8z3tj8g/wish/351745031