Question

Use the formula S_{n} = a_{1} * [ (1-r^{n}) / (1-r) ] to find the sum of the geometric series for the series:

1 - 2 + 4 - 8 ... and n = 7

Answer 1

The sum of the geometric series for the given series and n = 7 is 43.

Step-by-step explanation:

To find the sum of the geometric series 1 - 2 + 4 - 8 ... with n = 7, we can use the formula Sn = a1 * [ (1-rn) / (1-r) ].

In this series, the first term (a1) is 1 and the common ratio (r) is -2.

Plugging these values into the formula, we get S7 = 1 * [ (1-(-2)7) / (1-(-2)) ].

Simplifying the expression, we have S7 = 1 * [ (1-(-128)) / (1+2) ] = 1 * (129/3) = 43.

Therefore, the sum of the geometric series for the given series and n = 7 is 43.