Sunday, January 29, 2017

arithmetic progressions - How do I derive a formula for summation of this series?



I have a series in which the general term is represented by



an=kn+1knk+n(k1)2




where k is a constant.



How do I derive the formula for n=bn=1Sn (summation of n terms)?



I'm not really good at mathematics (high school level), so kindly explain it in the simplest way possible.


Answer



HINT



Note that you can divide and sum each part separately




an=kn+1knk+n(k1)2=kn+1k(k1)2nkn(k1)2=kn+1(k1)2k(k1)2n(k1)



and



n=bn=1kn+1=n=b1n=0kn+2=k2n=b1n=0kn=k21kb1k



n=bn=1n=b(b+1)2


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