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Integral test for Series
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Consider an integer N and a non-negative function f defined on the unbounded interval [N, ∞), on which it is monotone decreasing. Then the infinite series
\sum_{n=N}^\infty f(n)
converges to a real number if and only if the improper integral
\int_N^\infty f(x)\,dx
is finite. In other words, if the integral diverges, then the series diverges as well.
\sum_{n=N}^\infty f(n)
converges to a real number if and only if the improper integral
\int_N^\infty f(x)\,dx
is finite. In other words, if the integral diverges, then the series diverges as well.
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