https://padlet.com/dingyifeiair/yrsaef0qpuuq Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-15 16:53:57 UTC 2024-12-16 18:31:24 UTC hello@padlet.com dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729251 Proof using mathmatical induction, start with n=1, then n=k and n=k+1]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729251 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729252 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729252 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729254 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 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729254 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729256 use n=k and set it equal to n=k+1]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729256 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729257 It dont need calculator]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729257 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729259 Fibonacci number
Exponential series
Trigonometric series]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729259 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729260 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729260 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729262 Exponential series
use Euler's formula or expand the series and calculate it
Trigonometric series
Expand the series.]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729262 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729263 On e^x problems, don't round along the way.]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729263 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729264 i*pi is ln(-1)]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729264 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729265 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729265 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729266 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729266 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729268 Expand a binomial
use the Pascal's triangle
Use the formula from binomial formula]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729268 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729269 Choose the wrong row]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729269 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729270 Use calculator to expand the binomial.]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729270 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729271 A way to write a series in short]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729271 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729272 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729272 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729273 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 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729273 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729274 A series can convert to sigma notation for multiple ways.]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729274 dingyifeiair https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729275 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-15 16:53:57 UTC https://padlet.com/dingyifeiair/yrsaef0qpuuq/wish/351729275