Evaluate 9 sigma i=1 -28(-1/2)^i-1 using finite geometric sum formula. Round your answer to three decimal places
why did you use this?
S = 9(1 - (-1/2)^9) / (1 - (-1/2))
and that sum is not 60, in any case.
The problem said a = -28. So, you want
S = -28(1 - (-1/2)^9) / (1 - (-1/2)) = -1197/64
Apologies for the mistake. You are correct. Since the problem states that the first term (a) is -28, we can use the formula for the sum of a finite geometric series:
S = a(1 - r^n) / (1 - r)
Substituting the given values:
S = -28(1 - (-1/2)^9) / (1 - (-1/2))
= -28(1 - 1/512) / (1 + 1/2)
= -28(511/512) / (3/2)
= (-28 * 511 * 2) / (512 * 3)
= -28672 / 1536
= -1197 / 64
Therefore, the value of the sum of the given series is -1197/64.
To evaluate the sum using the finite geometric sum formula, we need to identify the values of the first term (a), the common ratio (r), and the number of terms (n).
In this case, the first term (a) is 9, the common ratio (r) is -1/2, and the number of terms (n) is 9.
The formula for the sum of a finite geometric series is:
S = a(1 - r^n) / (1 - r)
Substituting the values into the formula:
S = 9(1 - (-1/2)^9) / (1 - (-1/2))
= 9(1 - 1/512) / (1 + 1/2)
= 9(511/512) / (3/2)
= (9 * 511 * 2) / (512 * 3)
= 92088 / 1536
= 60
Therefore, the value of the sum of the given series is 60.