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

1 Answer
Surya K.
Mar 14, 2018

#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#.

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