Question
2.1.2 Given:
The sum of the first 20 terms of the series
is 1680 . Calculate the value of
.
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:
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:
The sum
Factor out
:
The sum of the first 20 natural numbers is:
So,
Given:
Solving for
:
Conclusion:
The value of is 3.
The value of
Answer:
The value of is 3.
The value of
Answered by UpStudy AI and reviewed by a Professional Tutor
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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: