# data[].attributes.body
Sigma Notation
Write a series in sigma notation
Go from sigma notation to an expansion of terms and find the sum

# data[].attributes.body
Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.

# data[].attributes.body
Approximate e^x, trig values, and logarithms of negative numbers
Euler's Formula
Natural number of a negative number
Fibonacci series

# data[].attributes.body
Use mathematical induction to prove the validity of mathematical statements
Used for both a series/sum and divisibility statements

# data[].attributes.body
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.

# data[].attributes.body
Expand a binomial (use Pascal's triangle to expand)
Find the designated term of each binomial expansion (use the sigma form of the binomial theorem

# data[].attributes.body
Find first five terms of an exponential series to find the value of e^x or trig series (use either the exponential series or trigonometric series)
Find the natural log of negative number as a complex number (use Euler's formula)

# data[].attributes.body
Series proof.
Divisibility proof.
Use 3 steps of induction.
Show n=1 works.
Assume n=k works.
Show n=k+1 works.

# data[].attributes.body
When forming a series to the sigma notation, do not forget to apply the formula and check your answer.

# data[].attributes.body
You must remember to include the minus as a negative symbol on the accompanying term when expanding.

# data[].attributes.body
On e^x problems, don't round along the way.

# data[].attributes.body
When adding k+1, make sure it is parenthesized; (K+1)

# data[].attributes.body
Get sigma on calculator for finite sums: Math button, then press Zero

# data[].attributes.body
Remember to find the middle numbers by adding the two values from directly above it. Apply the combinations formula for each problem. We should apply the idea of Pascal’s Triangle as well.

# data[].attributes.body
Make sure to add as much parenthesis as possible to get an accurate number. By misplacing one incorrectly, it can completely change the result because of PEMDAS. Using as much parenthesis as possible ensures the rule of PEMDAS.

# data[].attributes.body
When dividing the numbers, make sure to add parenthesis for both the numerator and the denominator because of PEMDAS.