Write the geometric series 9+3+1..... to 130 term in sigma notation
130
∑ 3^(3-k)
k=1
The general term is 3^(3 - n)
so ∑ (3)^(3-n) , were n = 1 to 130
To write the given geometric series in sigma notation, we need to determine the general formula for the terms of the series.
We observe that each term in the given series can be obtained by raising the common ratio, 1/3, to a certain power and then multiplying it by the first term, 9.
The n-th term of a geometric series can be calculated using the formula:
aₙ = a₁ * r^(n-1)
where aₙ represents the n-th term, a₁ is the first term, r is the common ratio, and n is the term number.
Applying this formula to the given series:
aₙ = 9 * (1/3)^(n-1)
Now, let's express the series in sigma notation:
∑[from n=1 to 130] (9 * (1/3)^(n-1))
In this notation, the "∑" symbol represents summation, the variable "n" represents the term number, and the numbers above and below the symbol denote the starting and ending values for n, respectively. The expression inside the parentheses represents the formula for each term of the series.