The sum of 1 - 1 + 1 - 1 + 1 - 1 ... to even number of terms is—
Correct Answer :
zero
Solution :
The correct option is zero.
We are given the infinite alternating series:
We need to find the sum of this series when taken up to an even number of terms.
Let us group the terms in pairs of two since the number of terms is even:
Evaluating each pair:
Thus, the sum becomes:
Therefore, the sum of the series to an even number of terms is zero.
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