400 Followers Problem - Reciprocal Summations 2

Calculus Level 5

S=(1+12+13)(14+15+16)+(17+18+19)(110+111+112)+\large{S = \left( 1 + \dfrac{1}{2} + \dfrac{1}{3} \right) - \left( \dfrac{1}{4} + \dfrac{1}{5} + \dfrac{1}{6} \right) + \left( \dfrac{1}{7} + \dfrac{1}{8} + \dfrac{1}{9} \right) - \left( \dfrac{1}{10} + \dfrac{1}{11} + \dfrac{1}{12} \right) + \ldots }

If SS can be expressed as:

ABCπD+ln(E)F\large{\dfrac{A\sqrt{B}}{C}\pi^D + \dfrac{\ln(E)}{F} }

for positive integers A,B,C,D,E,FA,B,C,D,E,F where gcd(A,C)=1\gcd(A,C)=1 and B,EB,E aren't any mthm^{th} power of a positive integer with mZ, m2m \in \mathbb Z, \ m \geq 2.

Submit the value of A+B+C+D+E+FA+B+C+D+E+F as your answer.


Also try these:
400 Followers Problem - Reciprocal Summations #1
400 Followers Problem - Reciprocal Summations #3
×

Problem Loading...

Note Loading...

Set Loading...