Does the series 1/4 - 1/2 +1 - 2 + converge or diverge. If it converges find the sum
since the terms get ever larger, it will diverge.
Sums are -1/4, 3/4, -5/4, 11/4, ...
To determine whether the series 1/4 - 1/2 + 1 - 2 + ... converges or diverges, we can analyze the pattern of its terms.
The given series is an alternating series, as the signs of the terms alternate between positive and negative. In order to determine convergence, we need to check two conditions: the terms should approach zero, and the absolute values of the terms should also decrease.
First, let's examine the absolute values of the terms:
|1/4|, |1/2|, |1|, |2|, ...
Notice that the absolute values of the terms do not decrease. In fact, they are getting larger as we move forward in the series. This violates the condition for convergence, as the terms should be decreasing in absolute value.
Since the series does not satisfy the condition that the absolute values of terms decrease, we can conclude that the series diverges.
Therefore, we do not need to find the sum, as the series does not converge.