(i) Estimate the sum for n = 10, 100 and 1000 (you may use computational tools to help, make sure to include supporting code). The image contains a mathematical expression involving a summation. The expression is written as:\[\sum_{i=1}^{n} \sin\left(\frac{i\pi}{n}\right) \cdot \frac{\pi}{n}\]This formula represents the sum of sine functions multiplied by a fraction involving $\pi$, iterated from $i = 1$ to $n$, where $n$ is an integer. The sine function is evaluated at $\frac{i\pi}{n}$ and then multiplied by $\frac{\pi}{n}$. This type of expression might appear in the context of numerical integration or Fourier analysis on an educational website.

For n=10 ∑i=110siniπ10π10=∑i=110siniπ10×π10=1.98352353751 (using desmos computational tool)…

Answered: Estimate the sum for n = 10, 100 and…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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(i) Estimate the sum for n = 10, 100 and 1000 (you may use computational tools to help, make sure to include supporting code).

The image contains a mathematical expression involving a summation. The expression is written as:

\[
\sum_{i=1}^{n} \sin\left(\frac{i\pi}{n}\right) \cdot \frac{\pi}{n}
\]

This formula represents the sum of sine functions multiplied by a fraction involving $\pi$, iterated from $i = 1$ to $n$, where $n$ is an integer. The sine function is evaluated at $\frac{i\pi}{n}$ and then multiplied by $\frac{\pi}{n}$. This type of expression might appear in the context of numerical integration or Fourier analysis on an educational website.

Expert Solution

Step 1

For n=10

$\sum_{i = 1}^{10} \sin (\frac{iπ}{10}) \frac{π}{10} = \sum_{i = 1}^{10} (\sin (\frac{iπ}{10}) \times \frac{π}{10}) = 1.98352353751 (using desmos computational tool)$

Supporting code: \sum_{i=1}^{10}\left(\sin\left(\frac{i\pi}{10}\right)\times\frac{\pi}{10}\right)

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