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

πŸš— Detecting Parking Lot Occupancy with Deep Learning and Faster R-CNN

-
Image
πŸš— Detecting Parking Lot Occupancy with Deep Learning and Faster R-CNN In this post, we’ll walk through how to build a parking lot occupancy detection model using PyTorch and the Faster R-CNN object detection architecture. We’ll use a COCO-style dataset (in this case, PKLot) that contains images of parking lots with annotations identifying parked vehicles. We'll explore how the model works, how to prepare your dataset and dataloader, and how to train and visualize predictions. πŸ“¦ Objective The goal is to detect whether a parking space is occupied by identifying cars in images. The system will learn to detect vehicles using annotated bounding boxes and classify each parking spot accordingly. 🧠 Model Architecture: Faster R-CNN Faster R-CNN is a popular two-stage object detection model: Region Proposal Network (RPN) suggests object-like regions. ROI Pooling + Classifier classifies and refines these region proposals. We use Faster R-CNN with a ResNet-50 FPN bac...
Read more

🎯 Building an Object Detection Model for MNIST with PyTorch (COCO-style Dataset)

-
Image
Object detection is one of the core tasks in computer vision, and in this post, we'll walk through a complete pipeline: from downloading and converting the MNIST dataset to COCO format, to building and training a custom object detector in PyTorch. We'll also visualize predictions, plot training history, and analyze failure cases! This project demonstrates how to: Convert a dataset to the COCO format. Build a lightweight CNN-based object detector. Train and validate the model with bounding box and class predictions. Evaluate model performance visually and statistically. πŸ”§ 1. Step-by-Step: Convert MNIST to COCO Format We’ll start by downloading MNIST and converting each digit into a COCO-style annotation: each image will have one bounding box and one label. πŸ—‚ mnist_download.py import torch import torchvision from torchvision import datasets import os import json from PIL import Image import numpy as np from tqdm import tqdm import matplotli...
Read more