# Powerful Patterns 4: Summation Fractions

## Look at the summations below. You should notice a pattern...

## The fractions have consecutive integers as numerators & denominators, but the denominators are less than the numerators by __1__! There's a formula for this unique summation pattern:

By the way, I printed the fractions in the summations above as *improper fractions* to make them easier to read. When the **numerator** is equal to the **denominator + 1**, the fraction can also be printed as a *mixed number* that's equal to **1 + 1/(the denominator)**.

Since **1** is the number of *multiplicative identity,* dividing by it gives you the dividend as the quotient & all integers are multiples of **1**! __If __**1** is the denominator, then the fraction is an integer! (*Algebraic fractions* don't count; an algebraic fraction is a fraction that has a non-integer for a numerator or denominator.)

### Speaking of patterns, maybe you already seen some other numerical math patterns that other mathematicians already discovered & published! (Besides me or you; any open-minded person can be a great mathematician, like me!)

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© Derek Cumberbatch