SOLUTION: Number Theory 2.(2017 Putnam)Evaluate the sum \[ \sum_{k=0}^{\infty} \left( 3\cdot \frac{ln(4k+2)}{4k+2}-\frac{ln(4k+3)}{4k+3}-\frac{ln(4k+4)}{4k+4}-\frac{ln(4k+5)}{4k+5} \righ

Question 1195429: Number Theory
2.(2017 Putnam)Evaluate the sum
\[
\sum_{k=0}^{\infty} \left( 3\cdot \frac{ln(4k+2)}{4k+2}-\frac{ln(4k+3)}{4k+3}-\frac{ln(4k+4)}{4k+4}-\frac{ln(4k+5)}{4k+5} \right)\] \hfill \break
\[=3\cdot \frac{ln2}{2}-\frac{ln3}{3}-\frac{ln4}{4}-\frac{ln5}{5}-\frac{ln6}{6}-\frac{ln7}{7}-\frac{ln8}{8}-\frac{ln93}{9}+3\cdot\frac{ln10}{10}-...
\]
\textbf{(As usual, ln $x$ denotes the natural logarithm of $x$.}
to translate to an image, go to https://artofproblemsolving.com/texer/nrqjrtmo
Answer by ikleyn(52785) (Show Source): You can put this solution on YOUR website!
.

For the solution, see this source (pdf-file)

https://www.maa.org/sites/default/files/pdf/Putnam/Competition_Archive/2017PutnamProblemsSolutions.pdf

part B4.

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