[일반] 수학질문 물어볼데 없어서 여기에 싸봄

[익명(211.204)]

https://www.wolframalpha.com/input/?i=sum+%282%28k+mod+2%29+-+1%29%2F%28n+%5E+k%29+k%3D1+to+inf

이게 결과가 저렇게 나오는이유가 뭐임?

[익명(211.184)]

sum (2(k mod 2) - 1)/(n ^ k) k=1 to inf = (sum 1/n^(2k-1) k=1 to inf) - (sum 1/n^2k k=1 to inf) = (sum (1/n^2k)*n k=1 to inf) - (sum 1/n^2k k=1 to inf) = n * (sum 1/n^2k k=1 to inf) - (sum 1/n^2k k=1 to inf) = (n - 1) * (sum 1/n^2k k=1 to inf) = (n - 1) * 1/n^2 * (sum 1/n^2(k-1) k=1 to inf) = (n - 1) * 1/n^2 * (1/(1-(1/n^2))) = (n - 1) * 1/n^2 * (n^2/(n^2-1)) = (n - 1) * (1/(n^2-1)

[익명(211.184)]

= (n - 1) / (n^2-1) = 1 / (n + 1)

[익명(211.184)]

등비수열 극한 조건에 의해서 |n|>1이어야함.

[감자양파링(219.254)]

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