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Mathematicians use Sigma Notation to represent the sum of a series

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

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Finding Fibonacci from formula
Know what the Fibonacci series is and why it is important.

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1) use mathematical induction to prove the validity of mathematical statements.
2) used for both series/sum and divisibility statements.

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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) Expand binomials using the Pascal's triangle.
2) Expand binomials using the Binomial Theorem.
3) Find a particular term of a binomial using the sigma form of the Binomial Theorem.

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Approximate e^x, trigonometric values, and logarithms of negative numbers by using series.
Rule: Xn=Xn-1 + Xn-2
Xn=term number
Xn-1=the previous term
Xn-2=the term before that

Exponential series: e^x=1+x+(x^2/2!)+(x^3/3!)...
Trigonometric series: cosx=1-(x^2/2!)+(x^4/4!)-(x^6/6!)...
sinx=x-(x^3/3!)+(x^5/5!)-(x^7/7!)...

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Be careful about the start point of the series.

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Be aware that n is one less than the term that we are calculating for in the Binomial Theorem.

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

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

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while doing the pascal triangle questions, draw the model on the side first.

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most of time calculate first three terms of series.
1 and x also include as first term.

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1) Series Proof
- show n=1
- assume n=k works
- show n=k+1 works
2) Divisibility Proof
- show n=1
- n=k
- n=k+1

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1) no basis step
2) wrong induction step

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1) calculator is not required
2) calculations include: foiling