Thursday, June 14, 2018

fractions - frac64times2+frac75times2+...+frac2119times2




I got this exercise from school and I have no idea what notion to use, it resumes to Harmonic series, I can't find a generic answer. Do you have any idea?



64×2+75×2+...+2119×2



Which is the generic answer for such a sum?


Answer



Consider the most general case A=bi=an2(n2)=12bi=ann2=12bi=an2+2n2 A=12bi=a1+bi=a1n2=(ba+1)+bi=a1n2 So, you are just left with the sum of fractions 14+15+16++119


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