Question

Determine whether the series –20 + 100 – 500 + ... is convergent or divergent

Answer 1

First get the general rule. What's the common multiple between terms? Divide a term by the number before it.

Answer 2

Since there is a common multiple, the series is geometric, and of the form
\[\Large a _{n}=a _{1} r ^{n-1}\]
a1 is the first term, r is the common multiple/ratio.

Note that a geometric series converges iff
\[\Large |r|<1\]

(absolute value of r has to be less than 1)

Answer 3

Understand...?

Answer 4

Yes, thank you.