Ruby has an Enumerable method called inject and it makes summing or getting the product of an array of values a snap. Below are some extended examples of it in use:

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#'injects' 0 in for sum before we start summing so 
#the result is 1+1+1
[1,1,1].inject(0) {|sum, value| sum+value}
#'injects' a value of 1 in for sum before we start summing so 
#the result is 1+1+1+1=4
[1,1,1].inject(1) {|sum, value| sum+value}
#nothing injected, so the first argument (sum) takes the 
#value of the first item in the array (1). The result here is 1+1+1=3. 
[1,1,1].inject() {|sum, value| sum+value}

#This will give you the product of the injected 0x1x1x1=0
[1,1,1].inject(0) {|product, value| product*value}
#This will give you the product of the injected 1x1x1x1=1
[1,1,1].inject(1) {|product, value| product*value}
#This will give you the product of the first value of the
#arrayx1x1=1
[1,1,1].inject() {|product, value| product*value}

So what does inject do?

1. The first argument of the block takes the value of the variable passed to inject (the injected variable) initially
2. After performing the block’s operation the result is stored in that same variable and at the end that final stored value is returned
3. If you don’t pass in a value to inject, the first argument of the block will initially take on the value of the first index in the array.

Read some more here: http://ruby-doc.org/core-2.1.3/Enumerable.html#method-i-inject

It can be made even shorter

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#This is equivalent to [1,1,1].inject(0) {|sum, value| sum+value} 
[1,1,1].inject(0,:+)
OR
[1,1,1].inject(:+)

The first argument is the injection, the second is calling on the symbol for the operator +. Symbol references to methods are also acceptable arguments for inject.

Summary

Instead of

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sum=0
array.each do {|value| sum+=value}

You can do this:

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array.inject(:+)

#inject and #reduce are the same method. I imagine reduce refering the to the collapsing of the array via the given block into one value