SOLUTION: find the sum of following series: n*1+(n-1)*2+(n-2)*3+.........+n*1

SOLUTION: find the sum of following series: n1+(n-1)2+(n-2)3+.........+n1

Question 174497: find the sum of following series:
n*1+(n-1)*2+(n-2)*3+.........+n*1
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!


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 =

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Combine the 1st and 3rd terms

 

The first sum is the arithmetic series of the first n positive
integers,

which is given by the formula: 

so we have

 

The remaining sum is the sum of the squares of the first n
positive integers.  This is also a well-known formula:



So now we have:



Rewrite the second term:



Factor out 

 

Get LCD in the right parentheses:













Edwin

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