**2014 SMO (Senior-Rd1) 16.** Evaluate the sum

.

Recall the definition of the factorial function: for non-negative integer ,

When faced with a series of many terms, try to * come up with an expression for the general term*. In this question, the required sum is the sum of

for . This looks like a term that can be simplified. Especially with fractions, a possible strategy is * to pull out as many factors as possible in the hope that there can be some common factors in the numerator and denominator*. These can be cancelled out. By pulling out common factors in the numerator:

and in the denominator:

The original expression can be greatly simplified:

Hence, the required sum is

The answer is **95**.

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