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Sagot :
The sum of the equation is = 5494000.
What does summation mean in math?
The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
Briefing:
Distribute 2j to (j+3).
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used.
The sum is 5,494,000.
Calculation according to the statement:
[tex]\sum_{j=1}^{200} 2 j(j+3)[/tex]
simplifying them we get:
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j[/tex]
Split the summation into smaller summations that fit the summation rules.
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j[/tex]
[tex]\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}[/tex]
The formula for the summation of a polynomial with degree 2
is:
[tex]\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}[/tex]
Substitute the values into the formula and make sure to multiply by the front term.
[tex](2)$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$[/tex]
we get: 5373400
Evaluating same as above : [tex]6 \sum_{j=1}^{200} j[/tex]
we get: 120600
Add the results of the summations.
5373400 + 120600
= 5494000
The sum of the equation is = 5494000.
To know more about summations visit:
https://brainly.com/question/16679150
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