Use the geometric series formula to find the sum of 1 – 2 + 4 – 8 + 16.
A) $\frac { ( - 2 ) ^ { 4 } - 1 } { ( - 2 ) - 1 }$
B) $\frac { 2 ^ { 4 } - 1 } { 2 - 1 }$
C) $\frac { ( - 2 ) ^ { 5 } - 1 } { ( - 2 ) - 1 }$
D) $\frac { 2 ^ { 5 } - 1 } { 2 - 1 }$

Question

Use the geometric series formula to find the sum of  1 – 2 + 4 – 8 + 16. 
A) $\frac { ( - 2 ) ^ { 4 } - 1 } { ( - 2 ) - 1 }$
B) $\frac { 2 ^ { 4 } - 1 } { 2 - 1 }$
C) $\frac { ( - 2 ) ^ { 5 } - 1 } { ( - 2 ) - 1 }$
D) $\frac { 2 ^ { 5 } - 1 } { 2 - 1 }$

Quizplus · Accepted Answer

The given series can be written as:

1 - 2 + 4 - 8 + 16 = 1 + (-2) + 4 + (-8) + 16

This is an alternating series with common ratio r = -2.

Using the formula for the sum of an alternating geometric series, we have:

S = a / (1 - r)

where a is the first term of the series.

In this case, a = 1 and r = -2, so:

S = 1 / (1 - (-2)) = 1 / 3

Therefore, the sum of the series 1 - 2 + 4 - 8 + 16 is:

1 - 2 + 4 - 8 + 16 = S = 1/3

The only answer choice that matches this result is C.

Use the Geometric Series Formula to Find the Sum of (−2)4−1(−2)−1\frac { ( - 2 ) ^ { 4 } - 1 } { ( - 2 ) - 1 }(−2)−1(−2)4−1​

Use the Geometric Series Formula to Find the Sum of $\frac { ( - 2 ) ^ { 4 } - 1 } { ( - 2 ) - 1 }$