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Uppercase Greek Letter Sigma. Used to find sum/sequence of multiple terms in an equation.

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

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Fibonacci Sequence represents many patterns found in nature.
Euler's method for e^x can be estimated through exponential series.
Trigonometric series and Euler's Formula sprout from this exponential series.

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Used to find validity of mathematical statements. Used in three steps. Can be used for both series/sum.

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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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Use Pascal's triangle to expand each binomial.
Find the (fifth) terms of (4a + 3b)^7

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Exponential series: for e^x, find 1 + x + ((x^2)/(2!))
Trigonometric series for cosine: for cos x, find 1 - ((x^2)/(2!)) + ((x^4)/(4!))
Trigonometric series for sine: for sin x, find x - ((x^3)/(3!)) + ((x^5)/(5!))
Euler's Formula: e^(ia) = cos a + i sin a
Remember that ln(-1) = i*pi

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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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When the sigma is infinity, we need to use formula S=a1/(1-r) to find the sum. Can not solve with calculator.

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When the title says Find the fourth or fifth term of a binomial, the result of "r" will always be the lesser amount of the term by 1.

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

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Make sure that, for the first part of step 3, make sure that you add the n=k and n=1 value before you move onto step two and find n=k+1

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

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Binomial theorem formula:
plug in certain values for exponents
put in correct order of the fraction (use parentheses).

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For Factorial (!): Press Math, then go to the PRB column, press 4, then press enter

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To find divisibility, you can use p = qr, p, q, r