PIL import Image import pytesseract

Load the uploaded image

image_path = "/mnt/data/1734011827003jhid82eb.jpg" image = Image.open(image_path)

Perform OCR to extract text

extracted_text = pytesseract.image_to_string(image, lang='rus+eng') extracted_textIt seems that the OCR didn't successfully extract the text from the image. I can still analyze the visible mathematical notation. Based on the uploaded image, the problem involves finding the sum of an infinite decreasing geometric progression.

The sum $S$ of an infinite geometric progression is calculated using the formula: $S = \frac{b_1}{1 - q}$ where:

• $b_1 = -3$ (the first term),
• $q = \frac{1}{4}$ (the common ratio).

Let me calculate this for you. Define the given values b1 = -3 # First term q = 1 / 4 # Common ratio

Calculate the sum of the infinite geometric progression

S = b1 / (1 - q) SThe sum of the infinite decreasing geometric progression is:

$S = -4$

Let me know if you’d like a detailed explanation of the calculation!

Related Questions:

1. What happens if $|q| \geq 1$ in a geometric progression?
2. How can we derive the formula for the sum of an infinite geometric series?
3. What are real-world applications of infinite geometric series?
4. Can we use this formula for a series where the first term $b_1$ is unknown?
5. What happens if $b_1$ is positive but $q$ is negative?

Tip:

When dealing with geometric progressions, always ensure $|q| < 1$ for the sum to converge to a finite value.