Question

Find the sum of the following series if the number of terms is 183 and the series is 4+(-4)+4+(-4).........?

Answer 1

`4`

Explanation:

We can solve this using inspection.

We see that the series is:

`4-4+4-4+4-4+4....`

We see that the first two terms give `0`. Working on the first four, six, and eight terms we get the same answer. Adding the first three, five and seven terms give us `4`.

We can say that if the series has an even number of items, it sums up to `0`, and if it has an odd number of terms, it sums up to `4`.

`183` is odd, and so the series sums up to `4`.