Mathematical Induction Fundamentals

Mathematical Induction Fundamentals

The Mathematical Induction Fundamentals are defined for applying 3 steps, such as step 1 for showing its initial ignite, step 2 for making an assumption, and step 3 for showing it is true based on the assumption. Make sure the Mathematical Induction Fundamentals should be used only when the question asks to use it.

Practice Questions

Basic Mathematical Induction Fundamentals

Prove \( 2+4+6+\cdots+2n = n(n+1) \) by mathematical induction.

Mathematical Induction with Indices

Prove \( 1 \times 2 + 2 \times 2^2 + 3 \times 2^3 + \cdots + n \times 2^n = (n-1) \times 2^{n+1} + 2 \) by mathematical induction.

Mathematical Induction with Factorials

Prove \( 2 \times 1! + 5 \times 2! + 10 \times 3! + \cdots + (n^2+1)n! = n(n+1)! \) by mathematical induction.

Mathematical Induction with Sigma \( \displaystyle \sum \) Notations

Prove \( \displaystyle \sum_{a=1}^{n} a^2 = \frac{1}{6}n(n+1)(2n+1) \) by mathematical induction.

Related Topics

Best Examples of Mathematical Induction Inequality
Best Examples of Mathematical Induction Divisibility
Mathematical Induction Inequality Proof with Factorials
Mathematical Induction Inequality Proof with Two Initials