An Alternating Series

Algebra Level 2

Determine the sum $(-1)^1 \cdot 2 + (-1)^2 \cdot 3 + (-1)^3 \cdot 4 + \cdots + (-1)^{98} \cdot 99 .$

Details and assumptions

The general term of this series is $(-1)^n \cdot (n+1)$ .

The answer is 49.

1 solution

Arron Kau Staff
May 13, 2014

When the exponent of $-1$ is even, the result of $(-1)^n$ is $1$ ; when the exponent is odd, $(-1)^n$ is $-1$ . We can group the terms in pairs to get $(-2 + 3) + (-4 + 5) + \cdots + (-98 + 99) .$ Each of the parenthetical sums is equal to $1$ , and there are 49 of them, so the overall sum is 49.

An Alternating Series

The answer is 49.

1 solution

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