We are tasked with finding the units digit of the sum \(1^1 + 2^2 + 3^3 + \dots + 2020^{2020}\).

To solve this, we need to observe the behavior of the units digits for powers of numbers and recognize patterns. Let’s break the process down.

### Step 1: Understanding Powers and Units Digits

Each number’s powers repeat in cycles for their units digits. Let's go over some examples to show how this works:

- **1^n**: The units digit is always 1 for any power of 1.
- **2^n**: The units digit follows a cycle: 2, 4, 8, 6, and repeats every 4 terms.
- **3^n**: The units digit follows a cycle: 3, 9, 7, 1, and repeats every 4 terms.
- **4^n**: The units digit alternates between 4 and 6 (cycle length 2).
- **5^n**: The units digit is always 5 for any power of 5.
- **6^n**

units digit of 1^1 + 2^2 + 3^3 + ... + 2020^2020

Discover how to determine the units digit of the sum 1^1 + 2^2 + ... + 2020^2020 using modular arithmetic and the cyclic nature of powers. This solution explores number theory and helps students in Grades 10-12 understand how to solve complex power-based problems.

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