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Learn what sigma notation is and how to use it
Write a series in sigma notation
Go from sigma notation to an expansion of terms and find the sum

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Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.

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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

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Some equations need to be proven to be an accurate equation representing a sequence. Induction is a way of proving.

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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.

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1 type of problem — expand (3x+4y)^3
Use the third row: 1, 3, 3, 1

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derived by replacing e^x with e^ia
i is the imaginary unit
a is the measure of an angle in radians
think back to Chapter 9

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Series proof.
Divisibility proof.
Use 3 steps of induction.
Show n=1 works.
Assume n=k works.
Show n=k+1 works.

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do the calculations correctly
make sure to know the differences n+1 or 1^n

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It is better to write every step down because expanding a binomial is a very complicated process.

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On e^x problems, don't round along the way.

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Make sure you plug in the right numbers or variables.

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Get sigma on calculator for finite sums: Math button, then press Zero

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Don’t just plug it in; solve it on paper.

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there are many equations that you dont need to calculate
such as, a+bi = r(cos 0 + isin 0)

r(cos 0 + isin 0) is called the polar form
rei0 is called exponential form of a complex number

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there is no calculator tips for this one, except plugging numbers.
Equations and other formulas that are included.