Saturday, 1 February 2014

summation - Why is sumnj=1dfrac1n=1



I encountered nj=11n=1 in my textbook, but I do not understand why this summation =1. My textbook provides no reasoning as to why this is the case.




My understanding is that, since there is nothing in 1n that depends on j, it seems that we are just summing 1n to itself up to n. However, I'm not sure how to interpret this and how it equals a value of 1.



I apologise if there is already a question on this, but my searches have encountered nothing that addresses this specific summation. If I am mistaken, I would appreciate it if someone could please redirect me.



I would greatly appreciate it if people could please take the time to explain the reasoning behind this.


Answer



Note that
nj=11n=n times1n+1n++1n=n1n=1



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