What is the maximum possible value of #k# for which 2013 can be written as a sum of #k# consecutive positive integers?

1 Answer
Tony B
Mar 25, 2017

4025

Explanation:

Key points

Positive integer values.

#ul("Maximum")# count of #ul("consecutive")# values that are summed

To be a maximum count means that you have to start at the lowest positive value, which is 1
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Mean value times the count of values = 2013

Starting at 1 means that the last value is the same as the count of values so we have:

#=> (1+k)/2=2013#

#=>1+k=4026#

#=>k=4025#

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