Thursday, 22 October 2015

summation - Easy question regarding this proof




I do not understand a small step in a proof I'm reading at the moment. Why are the following things equal?



nk=112k112nk=11k=2nk=11knk=11k


Answer



Separating out the odd & the even terms in the denominator,
2nk=11k=nk=1(12k1+nk=112k)



=nk=112k1+nk=112k




=nk=112k1+12nk=11k


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