https://padlet.com/aablanco4009/3jrc6p3dyt63 Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-16 15:13:00 UTC 2023-08-09 07:35:55 UTC hello@padlet.com aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005240 Use mathematical induction to prove the validity of mathematical statements
Used for both a series/sum and divisibility statements]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005240 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005244 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005244 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005247 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 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005247 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005250 When adding k+1, make sure it is parenthesized; (K+1)]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005250 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005252 When dividing the numbers, make sure to add parenthesis for both the numerator and the denominator because of PEMDAS.]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005252 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005255 Approximate e^x, trig values, and logarithms of negative numbers
Euler's Formula
Natural number of a negative number
Fibonacci series]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005255 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005258 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005258 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005260 Find first five terms of an exponential series to find the value of e^x or trig series (use either the exponential series or trigonometric series)
Find the natural log of negative number as a complex number (use Euler's formula)]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005260 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005263 On e^x problems, don't round along the way.]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005263 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005265 Make sure to add as much parenthesis as possible to get an accurate number. By misplacing one incorrectly, it can completely change the result because of PEMDAS. Using as much parenthesis as possible ensures the rule of PEMDAS.]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005265 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005267 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005267 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005270 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005270 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005273 Expand a binomial (use Pascal's triangle to expand)
Find the designated term of each binomial expansion (use the sigma form of the binomial theorem]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005273 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005274 You must remember to include the minus as a negative symbol on the accompanying term when expanding.]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005274 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005275 Remember to find the middle numbers by adding the two values from directly above it. Apply the combinations formula for each problem. We should apply the idea of Pascal’s Triangle as well.]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005275 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005276 Sigma Notation
Write a series in sigma notation
Go from sigma notation to an expansion of terms and find the sum]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005276 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005277 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005277 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005278 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 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005278 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005279 When forming a series to the sigma notation, do not forget to apply the formula and check your answer.]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005279 aablanco4009 https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005280 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-16 15:13:00 UTC https://padlet.com/aablanco4009/3jrc6p3dyt63/wish/352005280