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[Error](https://www.wolframalpha.com/input?i=sum%28%28-1%29%5Ek%2F%28k%5E2%2B2*k%2B2%29%2Ck%2C0%2Cinf%29%3B) It is gives $$\sum_{k=0}^{\infty}\frac{(-1)^k}{k^2+2k+2}\approx 0.363998$$ but exact value: ...