Seemingly Hard Summation

Algebra Level 4

Find ∑ k = 1 ∞ ( − 1 ) k − 1 k ∑ n = 0 ∞ 300 k ( 2 n ) + 5 \sum_{k=1}^{\infty} \frac{(-1)^{k-1}}{k} \sum_{n=0}^{\infty} \frac{300}{k(2^n)+5}

139 139 ∞ \infty 138 138 200 200 137 137 150 150

ChengYiin Ong by ChengYiin Ong , 17, Malaysia

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