**Mathematics and Programming: Implementing a Summation Function**This section involves completing the function `calculate`, which computes and returns the value of a specific summation for given arguments, $ x $ and $ n $.### Mathematical DefinitionThe sum is defined as:\[\sum_{i=1}^{n} \left( \frac{i^2}{x^i} \times 2^i \right) = \left( \frac{1^2}{x^1} \times 2^1 \right) + \left( \frac{2^2}{x^2} \times 2^2 \right) + \left( \frac{3^2}{x^3} \times 2^3 \right) + \ldots + \left( \frac{n^2}{x^n} \times 2^n \right)\]Where $ n \geq 1 $.### Examples| Function Call | Return Value ||----------------------|-------------------------------|| `calculate(5, 4)` | 2.0256000000000003 || `calculate(2, 7)` | 140.0 || `calculate(7, 2)` | 0.6122448979591837 || `calculate(3, 9)` | 22.196311537875324 |### Code Implementation```pythondef calculate(x, n): return 0 # DELETE THIS LINE and start coding here. # Remember: end all of your functions with a return statement, not a print statement!# Test casesprint(calculate(5, 4))print(calculate(2, 7))print(calculate(7, 2))print(calculate(3, 9))```In this coding problem, you need to replace the placeholder `return 0` with the logic that computes the defined summation. After implementing the function, you can test it using the provided test cases.### Explanation of the Task1. **Function Definition**: The function `calculate` takes two parameters: `x` and `n`.2. **Summation Logic**: To compute the summation, the function must loop over the range from 1 to `n`, evaluating the expression for each $ i $ and accumulating

function in python:- A chunk of code known as a function only executes when it is invoked. Data that…

Complete the function calculate, which computes and returns the value of the following sum for the given arguments, x and n. n Σ ( ² × ²¹) = ( ² × ²¹ ) + ( ²⁄² × ²² ) + ( ³³² × ²³) + - + ( ² × ²¹) ... i=1 Assume n ≥ 1. Examples: Function Call calculate (5,4) calculate (2,7) Return Value [ ] 2.0256000000000003 140.0 calculate (7,2) 0.6122448979591837 calculate (3,9) 22.196311537875324 1 def calculate (x, n): 2 3 4 5 # Test cases 6 print (calculate (5, 4)) 7 print (calculate (2, 7)) return 0 # DELETE THIS LINE and start coding here. # Remember: end all of your functions with a return statement, not a print statement! 8 print (calculate (7, 9 print (calculate (3, 2)) 9))

Complete the function calculate, which computes and returns the value of the following sum for the given arguments, x and n. n Σ ( ² × ²¹) = ( ² × ²¹ ) + ( ²⁄² × ²² ) + ( ³³² × ²³) + - + ( ² × ²¹) ... i=1 Assume n ≥ 1. Examples: Function Call calculate (5,4) calculate (2,7) Return Value [ ] 2.0256000000000003 140.0 calculate (7,2) 0.6122448979591837 calculate (3,9) 22.196311537875324 1 def calculate (x, n): 2 3 4 5 # Test cases 6 print (calculate (5, 4)) 7 print (calculate (2, 7)) return 0 # DELETE THIS LINE and start coding here. # Remember: end all of your functions with a return statement, not a print statement! 8 print (calculate (7, 9 print (calculate (3, 2)) 9))

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Declaring and Defining the function

A set of statements, which performs a particular task is called a function. The program gains modularity by using function. The application is quite easy to understand, read, and edit when they are created with functions. The developer/programmer creates a function and uses main() to call the function. Once the function gets executed, the control is transferred to the main program.

Question

**Mathematics and Programming: Implementing a Summation Function**

This section involves completing the function `calculate`, which computes and returns the value of a specific summation for given arguments, $ x $ and $ n $.

### Mathematical Definition

The sum is defined as:

\[
\sum_{i=1}^{n} \left( \frac{i^2}{x^i} \times 2^i \right) = \left( \frac{1^2}{x^1} \times 2^1 \right) + \left( \frac{2^2}{x^2} \times 2^2 \right) + \left( \frac{3^2}{x^3} \times 2^3 \right) + \ldots + \left( \frac{n^2}{x^n} \times 2^n \right)
\]

Where $ n \geq 1 $.

### Examples

| Function Call | Return Value |
|----------------------|-------------------------------|
| `calculate(5, 4)` | 2.0256000000000003 |
| `calculate(2, 7)` | 140.0 |
| `calculate(7, 2)` | 0.6122448979591837 |
| `calculate(3, 9)` | 22.196311537875324 |

### Code Implementation

```python
def calculate(x, n):
return 0 # DELETE THIS LINE and start coding here.
# Remember: end all of your functions with a return statement, not a print statement!

# Test cases
print(calculate(5, 4))
print(calculate(2, 7))
print(calculate(7, 2))
print(calculate(3, 9))
```

In this coding problem, you need to replace the placeholder `return 0` with the logic that computes the defined summation. After implementing the function, you can test it using the provided test cases.

### Explanation of the Task

1. **Function Definition**: The function `calculate` takes two parameters: `x` and `n`.
2. **Summation Logic**: To compute the summation, the function must loop over the range from 1 to `n`, evaluating the expression for each $ i $ and accumulating

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