https://padlet.com/darcywang0109/s9fwrbj23qds Sections 12.5, 12.6, 12.7, 12.9 en-us 2019-04-15 17:33:12 UTC 2026-01-11 19:59:09 UTC hello@padlet.com darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745178 Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number. 

]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745178 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745179 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745179 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745182 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 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745182 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745185 Don't just add a term in one side, you have to add it in both side to keep the equation equivalent. ]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745185 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745187 Type everything on the calculator carefully, use parentheses.  ]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745187 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745189 The Fibonacci sequence describes many patterns of numbers found in
nature.
Euler number can be expressed as the sum of the infinite series.]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745189 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745192 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745192 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745193 Use the first five terms of the exponential series and a calculator to approximate the value.
1) Use exponential series.  Change the x to the power. 
2) Calculate those terms on calculator. ]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745193 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745196 On e^x problems, don't round along the way.]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745196 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745198 Plug everything on calculator carefully, don't forget to use parentheses. ]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745198 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745203 Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745203 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745207 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745207 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745208 1)Use Pascal's triangle to expand binomials.
2)Use the Binomial Theorem
3)Find a particular term of a binomial using the sigma form of the Binomial Theorem

]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745208 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745210 Forget to times the Pascal's triangle numbers.]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745210 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745212 Get factorial on calculator for a specific term: Type the number you want to do factorial first. Click math button, go to the PROB, then choose number 4, which is !. ]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745212 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745215 The sigma symbol can be used all by itself to represent a generic sum the general idea of a sum, of an unspecified number of unspecified terms.]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745215 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745216 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745216 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745219 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 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745219 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745220 It is not always starting with n=1.]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745220 darcywang0109 https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745222 Get sigma on calculator for finite sums: Math button, then press Zero]]> 2019-04-15 17:33:12 UTC https://padlet.com/darcywang0109/s9fwrbj23qds/wish/351745222