SOLUTION: simplify the following expressions 1) i^2014!+i^2013!+i^2012!+i^2011!+i^2010!+...+i^2!+i^1!

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Question 897746: simplify the following expressions
1) i^2014!+i^2013!+i^2012!+i^2011!+i^2010!+...+i^2!+i^1!
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


All the factorials in the exponents are multiples of 4 except the last three.

When i is raised to the power of any multiple of 4, the result is 1. 

That's because  
 
So the above becomes:



There are 2014-3 or 2011 1's, and for the last three terms





So the sum is 

Edwin
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