Question

Determine if the summation (to be posted below) is convergent or divergent through the alternating series test.

Answer 1

\[\sum_{n=1}^{\infty}(-1)^n(\sqrt{n+1}-\sqrt{n})\]

Answer 2

when they state the alternating series test in my textbook they have the -1 to the power of n-1 not n so I have to change it to
\[\sum_{n=1}^{\infty}(-1)^{n-1}(\sqrt{n}-\sqrt{n+1})\]
right?

Answer 3

but thats increasing so how am I suppose to use AST?

Answer 4

Either way, it's decreasing absolutely.

Answer 5

heres the thing the instructor said to use the concepts they introduced in that section to answer these questions. All they introduced this section was the AST

Answer 6

Just check if \[|\lim_{n \rightarrow \infty} \frac{ A _{n+1} }{ A _{n} } |<1\]

Answer 7

I know the ratio test but unfortunately I can't use that yet. Its introduced in a later section in the textbook