## 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**