Find the sum of

where .

Source: NCTM Mathematics Teacher, February 2006

**SOLUTION
**

Multiply both sides by

The above expression has terms with the middle term equal

We combine the first term to the last term, the second to the next to last and so on

We end up with seven terms, six terms and the middle term . The six terms cancel the six terms leaving the remaining two terms .

**Answer**:

*Alternative solution
*

We combine the terms in pairs

We end up with thirteen terms and the remaining term

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