Mathematics: What is the expanded notation fraction of 810.435

What is the expanded notation fraction of 810.435

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abelxoconda

28.12.2022

The series is represented by sum $f(n) = 2 \cdot \Sigma\limits_{i=0}^{n} n$ , $n \in\mathbb{N }$ . The remaining element of the series is 30.

Step-by-step explanation:

This exercise consist in deriving the function which contains every element of the given series. The sum that contains all elements of the series { 0, 2, 6, 12, 20,...} is represented by the following formula:

$f(n) = 2 \cdot \Sigma\limits_{i=0}^{n} n$ , $n \in\mathbb{N }$ (1)

Where is the cardinal associated with the element of the series.

Lastly, we proceed to evaluate the sum for the first five elements:

n = 0

f(0) = 0

n = 1

f(1) = 0 +2

f(1) = 2

n = 2

f(2) = 0 + 2 + 4

f(2) = 6

n = 3

f(3) = 0 + 2 + 4 + 6

f(3) = 12

n = 4

f(4) = 0+2+4+6+8

f(4) = 20

The series is represented by sum $f(n) = 2 \cdot \Sigma\limits_{i=0}^{n} n$ , $n \in\mathbb{N }$ .

Lastly, the missing element is found by evaluating the function at n = 5 , that is:

n = 5

f(5) = 0 + 2 + 4 + 6 + 8 + 10

f(5) = 30

The remaining element of the series is 30.

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What is the expanded notation fraction of 810.435

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