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A mathematical proof technique.
It is essentially used to prove that a property P(n) holds for every natural number n, i.e. for n = 0, 1, 2, 3, and so on.
The method of inductionrequires two cases to be proved.

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A description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

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

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A series can be represented in a compact form.
The Greek capital letter, ∑ , is used to represent the sum. The series 4+8+12+16+20+24 can be expressed as 6∑n=14n .
The expression is read as the sum of 4n as n goes from 1 to 6 .

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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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First five terms of the exponential series. E^2.03
E^2.03=1+2.03+2.03^2/2 + 2.03^3/3! + 2.04^4/4!
=7.19

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(2x-y)^6
64x^6-192x^5y+240x^4y^2-160x^3y^3+60x^2y^4-12xy^5+y^6

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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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Make sure to check the both formula is correct after following steps.

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

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Make sure to start with k = something to the n.

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Make sure to keep increasing by one.

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We don't have to use the calculator but be careful with distributing those number correctly.

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Make sure to use correct sign and numbers on the calculator otherwise, the result will be wrong

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When you calculate make sure you multiply the numbers on the pascal's number too.

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