# Which of the following statements are​ true?i.If a_{n} and f(n) satisfy the requirements of the integral test, then \sum_{n=1}^{\infty} a_n = \int_1^{\infty} f(x)dx.ii.

Which of the following statements are​ true?
i.If $$a_{n}\ \text{and}\ f(n)$$ satisfy the requirements of the integral test, then $$\sum_{n=1}^{\infty} a_n = \int_1^{\infty} f(x)dx$$
ii. The series $$\sum_{n=1}^{\infty} \frac{1}{n^p}\ \text{converges if}\ p > 1\ \text{and diverges if}\ p \leq 1$$.
iii. The integral test does not apply to divergent sequences.

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Nathanael Webber

1)If $$a_n$$ and f(n) satisty the requirements of the integral test, then $$\sum_{n=1}^{\infty} a_n = \int_1^{\infty} f(x)dx$$
2)The series $$\sum_{n=1}^{\infty} \frac{1}{n^p}\ \text{converges if}\ p > 1\ \text{and diverges if}\ p \leq 1$$.
3) The integral test can be applied to both covergent and divergent testedherefore E.Only statements 1 and 2 are true.

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