# Calc6.6

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Explain why the integral test is or is not applicable to $\sum _{{n=1}}^{{\infty }}-{\frac {1}{n^{2}}}$.

The integral test states a function must be continuous, positive, and decreasing. This function is continuous but it is negative and increasing. However, we can easily use the integral test. Instead, look at the function $f(x)={\frac {1}{x^{2}}}$. This function is continuous, positive, and decreasing on the interval $[1,\infty ]$ so the integral test applies. In fact, the integral test confirms that its series converges. Thus, since this series converges, multiplying every term by -1 will simply change the sign of the sum but will not affect convergence at all and this is all we need to show to know that the given series converges.