Question
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2.1.2 Given: The sum of the first 20 terms of the series
is 1680 . Calculate the value of .

Ask by Vaughn Lynch. in South Africa
Jan 30,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The value of is 3.

Solution

Let’s break down the problem step by step to find the value of .
Given Series:
Understanding the Series:
Each term in the series can be expressed as:
where is the term number (starting from 1).
Sum of the First 20 Terms:
The sum of the first 20 terms is:
Factor out :
The sum of the first 20 natural numbers is:
So,
Given:
Solving for :
Conclusion:
The value of is 3.
Answer:
The value of is 3.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Extra Insights

To solve for , we first recognize the series given:
We can factor out :
The sum of the first 20 natural numbers can be calculated using the formula:
where :
Substituting this back into our expression, we get:
According to the problem, the sum of the first 20 terms equals 1680:
Now, to isolate , divide both sides by 210:
We know that can be expressed as :
Thus, we conclude:
Therefore, the value of is:

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