U9 Series(KA/PRE/U9)

-

Unit 9: Series

Geometric Series

A geometric series adds numbers that multiply by the same amount each time. Example: 1 + 2 + 4 + 8 + 16...

Geometric Series (with Summation Notation)

We can write a geometric series like this: Σ (from n = 0 to N) of arⁿ This is called summation notation.

Arithmetic Series

An arithmetic series adds numbers that increase by the same amount each time. Example: 2 + 4 + 6 + 8 + 10...

The Binomial Theorem

The binomial theorem helps us expand expressions like (a + b)ⁿ. It's like a recipe to figure out all the terms!

Quiz: Test Your Understanding

If we start with 1 and double each time, what is the 4th number?

  1. 4
  2. 8
  3. 16

Comments

Post a Comment

Popular posts from this blog

🧠 Building a Korean Character Recognition Model with PyTorch

-
Image
Hangul, the Korean writing system, is both elegant and systematic. Each character is a combination of components called Jamo: μ΄ˆμ„± (initial), 쀑성 (medial), and μ’…μ„± (final). In this project, I built a deep learning model using PyTorch to recognize these components from rendered character images. Here's how I did it. ✨ Project Overview This project involves: Generating synthetic images of Hangul characters with their bounding boxes. Decomposing characters into Jamo components. Training a convolutional neural network to classify each character's μ΄ˆμ„±, 쀑성, and μ’…μ„±. Performing inference on single or multiple images and visualizing the results. Let’s break it down. πŸ—️ Step 1: Generate Hangul Character Dataset We use a TrueType font (like Malgun Gothic ) to render images of Hangul syllables and compute their bounding boxes. Each image is saved along with Jamo annotations in JSON. generate_korean_chars.py from PIL import Image , ImageDraw , ImageFont import os i...
Read more

πŸ“ Fun Fruit Math Game for Kids – Learn Multiplication & Division with Smiles!

-
Image
πŸ“ Fruit Math Game 🍌 Check πŸ“ Fun Fruit Math Game for Kids – Learn Multiplication & Division with Smiles! Learning math can be fun—especially when fruits and emojis get involved! πŸŽ‰ If you're looking for a simple, colorful way to help elementary school students practice multiplication and division, this interactive Fruit Math Game is perfect for you. πŸ‘Ά Who's it for? This game is designed for: Elementary school students (Grades 1–3) Kids just starting to learn multiplication and division Parents or teachers looking for fun math learning tools 🧠 What does it teach? The game randomly generates problems for: Multiplication (e.g. 3 × 2) Division (e.g. 12 ÷ 4) Instead of just numbers, it uses fruit emojis like πŸŽπŸŒπŸ“ to make math more visual and engaging. ✨ Key Features Colorful fruit emojis Randomized math problems Instant feedback (correct or try again!) Kid-friendly design πŸ–₯️ How to Use Copy th...
Read more

Visualize Permutations and Combinations with Fruits!

-
Image
Fruit Permutation & Combination Visualizer Select number of fruits (n): Generate 🍎 Apple 🍌 Banana πŸ‡ Grapes πŸ“ Strawberry 🍍 Pineapple Combinations (order doesn't matter) Permutations (order matters) Have you ever wondered how many different ways you can arrange fruits when choosing some from a basket? Today, let’s explore permutations and combinations with a fun and simple program using fruit emojis! 🍏 What You Will Learn The difference between permutations and combinations How to calculate them How to see them visually using fruit icons! πŸ₯§ Meet the Fruits We have five fruits in our basket: 🍎 Apple 🍌 Banana πŸ‡ Grapes πŸ“ Strawberry 🍍 Pineapple You can choose any number of fruits from 1 to 5. Once you choose, the program shows you: All combinations (order doesn’t matter) All permutations (order ma...
Read more