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Sigma notation allows us to write a long sum in a single expression

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

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Approximate e^x, trigonometric values, and logarithms of negative numbers by using series.

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Use mathematical induction to prove the validity of mathematical statements.
Do this both for a 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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Expand (x+y)^6
x^6+6(x^5 )y+15(x^4)(y^2)+20(x^3)(y^3）+15（x^2)(y^2)+6xy^5+y^6

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Find ln(-3) to four decimal places.
ln(-1)+ln(3)
=iPi+ln(-1)
=Ipi+1.0936

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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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By using the formulas given above in exactly the form that they are given.

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Make sure to remember the pascal's triangle and mind about the positive and negative coefficient.

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

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Make sure to check if it is valid if it matches for both sides.

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

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No

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Make sure to use Ln and take the natural log for both sides.

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No