I can't figure out how to find the n on top of the sigma. I have the rest of the equation but I just don't know what to do. I'll use "E" for sigma.
nEi=1 (-5+7i)=486
Can someone please show me how to do this problem?
To find the value of the "n" on top of the sigma symbol (Σ), we need to understand what the sigma symbol represents.
In mathematics, the sigma symbol (∑) is used to denote summation. It allows you to add up a series of terms in a concise way. The expression below the sigma symbol determines the values of the index variable, and the expression on the right side of the equality sign represents the terms to be summed.
Let's break down the given expression:
nΣi=1 (-5 + 7i) = 486
Here, we have a summation from i=1 to n of the expression (-5 + 7i). The index variable "i" takes on values starting from 1 up to "n." Our goal is to find the value of "n" that satisfies the equation.
To solve this problem, we need to evaluate the summation expression and solve for "n".
Let's begin by expanding the summation:
(-5 + 7 * 1) + (-5 + 7 * 2) + (-5 + 7 * 3) + ... + (-5 + 7 * n) = 486
Now, simplify each term within the summation:
-5 + 7 + (-5 + 14) + (-5 + 21) + ... + (-5 + 7n) = 486
Combine like terms:
(7n - 5) + (7n - 5) + ... + (7n - 5) + 7 = 486
Since all the terms within the summation are the same (7n - 5), we can simplify further:
n(7n - 5) + 7 = 486
Distribute the "n" to the terms inside the parentheses:
7n^2 - 5n + 7 = 486
Rearrange the equation into a quadratic form:
7n^2 - 5n - 479 = 0
Now, we can solve this quadratic equation using various methods such as factoring, completing the square, or using the quadratic formula.
Once you find the solutions for "n", remember to check if they make sense within the context of the problem, such as if they are positive whole numbers or integers.
Please provide the coefficients and we can continue solving the quadratic equation.