Discussion
The sum of \(5 - 5 + 5 - 5 + 5 - 5\) ......, to odd number of terms is :
Answer: D
The sum is 5.
Group the terms in pairs: each pair 5 - 5 gives 0. With an odd number of terms, all but the last term pair off, and the last term is a +5:
\[ \begin{aligned} 5 &= 5 \ (1\ \text{term}) \\ 5 - 5 + 5 &= 5 \ (3\ \text{terms}) \\ 5 - 5 + 5 - 5 + 5 &= 5 \ (5\ \text{terms}) \end{aligned} \]
The answer 0 holds for an even number of terms, and -5 would need the series to end on a minus term; 15 is the sum of the positive terms only for five terms, ignoring the subtractions.
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