Help with summation from a Expected Value problem

Dec 2019
1
0
San Diego
Hi,

Could anyone explain to me how the summation became the equation on the right?

Any help would be much appreciated!!
 

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romsek

MHF Helper
Nov 2013
6,671
3,005
California
this is a series over $j$ so you can bring the $\dfrac 1 k$ outside the summation.

then it's a pretty common summation result that

$\sum \limits_{j=1}^k = \dfrac{k(k+1)}{2}$

It's not hard to see this

$1 + 2 + 3 + \dots k = (1+k) + (2+(k-1)) + (3+(k-2)) \dots = (k+1) + (k+1) + (k+1) + \dots = \dfrac{k}{2}(k+1)$
 
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