- #1
rkell48
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Homework Statement
In each case, x is an integer between -6 and 6 inclusive.
Homework Equations
x
Σ 2i =12
i=1
The Attempt at a Solution
2x1 = 12 + 2x2 = 12 +...+2x(x) = 12
NascentOxygen said:I surmise you to be saying x is an integer and lies somewhere between -6 and +6. Correct?
So I'd read it as the sum of all terms, 2*i
for all integer values i starting from 1 and stepping through to x
but stopping when that sum equals 12.
rkell48 said:Homework Statement
In each case, x is an integer between -6 and 6 inclusive.
Homework Equations
x
Σ 2i =12
i=1
The Attempt at a Solution
2x1 = 12 + 2x2 = 12 +...+2x(x) = 12
Sigma notation is a mathematical shorthand notation used to represent the sum of a series of numbers. It is denoted by the Greek letter sigma (Σ) and has a lower and upper limit, with the numbers inside the sigma representing the values to be summed.
To interpret sigma notation, you start by replacing the variable (usually represented by "i") with the lower limit value. Then, you evaluate the expression inside the sigma using this value. Next, you replace the variable with the next consecutive value and evaluate the expression again. This process continues until the upper limit is reached, and then you add up all the evaluated values to get the sum.
The top value in sigma notation represents the upper limit or the final value that the variable will take before the expression is evaluated. This value is typically indicated by a number or another variable.
When the top value in sigma notation is x, you will need to first find the value of x. This can be done by solving the expression inside the sigma using the given variable. Once you have the value of x, you can then follow the steps for interpreting sigma notation to find the sum.
Yes, sigma notation can be used for any type of series as long as there is a pattern or rule for determining the values to be summed. It is commonly used in mathematics, physics, and other sciences to represent infinite series, sequences, and other mathematical operations.