# 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.

Series

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

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 $$\sum_{n=1}^{\infty} \frac{1}{n^p}\ \text{converges if} p > 1\ \text{and diverges if}\ p \leq 1$$.