Mathematical induction is a method of mathematical proof. A series is the cumulative sum of a given sequence of terms in mathematics. These terms are typically real or complex numbers, but they can be much more general.

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Series & Mathematical Induction:

Mathematical induction is used to prove general structures such as trees termed as Structural Induction. This structural induction is used in computer science like recursion. Also, it is used for correctness proofs for programs in computer science.

Real-life Application of Series & Mathematical Induction

Series

Calculating the payment for a car, mortgage, or any loan in general.

Saving for retirement, or simply saving by making deposits in a bank or other interest-bearing account (I suppose we could include investing in general as well).

Pricing insurance and annuities. Reserving too. More broadly, any kind of business planning involving the NPV of future cashflows.

Mathematical Induction

When the very first domino topples, it will lean against the second domino and make it fall. Ensure that each domino will hit the domino next to it and that each hit makes a domino fall. If conditions (1) and (2) are satisfied, then all the dominoes will fall, proving the principle of mathematical Induction.

Sub-Topics List:

Sequences & Series

Mathematical Induction

Pascal’s Triangle

The Binomial Theorem

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The hardest arithmetic to master is that which enables us to count our blessings
Eric Hoffer

references

Sub-Topics

Sequences & Series

Sequences and Series play an important role in various aspects of our lives. They help us predict, evaluate and monitor the outcome of a situation or event and help us a lot in decision making.

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Mathematical Induction

The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science.

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Pascal’s Triangle

One real life situation that Pascal’s Triangle is used for is Probability, and combinations. We have situations like this all of the time. For example, say you are at an ice cream shop and they have 5 different ice creams. You want to know how many different ways you can pick two of the ice creams and eat them.

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The Binomial Theorem

The binomial theorem is used heavily in Statistical and Probability Analyses. It is so much useful as our economy depends on Statistical and Probability Analyses. In higher mathematics and calculation, the Binomial Theorem is used in finding roots of equations in higher powers.

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