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Infinite Series of Real Numbers (Cesaro summable)© BrainMass Inc. brainmass.com March 6, 2023, 12:45 pm ad1c9bdddf
a) (I'm led to believe that there is a typo in the submitted question. It is confirmed with this pdf: www.csun.edu/~hcmth017/hw451.pdf)
LHS is the (corrected) definition of Cesaro summabilty expanded. The RHS is also expanded by applying the definition of sn (line 3). All of the ak's are grouped together (line 4) 1/n is distributed over all of the terms (note that the an-1 term occurs once but its form is to maintain the pattern). ...
This is a proof regarding a Cesaro summable series.