Question

Determine if the series is convergent or divergent 20-15+10-5....

Answer 1

Answer:

Option b is correct.

The series 20-15+10-5....is Divergent

Step-by-step explanation:

Alternating series Test:

$\sum_{n=1}^{\infty} (-1)^{n-1} (b_n) =b_1-b_2+b_3-........$

$b_n>0$ satisfies:

• $b_{n+1} \leq b_n$   for all n

• $\lim_{n\rightarrow \infty} b_n = 0$

Then the series converges,

otherwise diverges.

Given the series: 20-15+10-5....

This is a alternating series:

$\sum_{n=1}^{\infty} (-1)^{n-1} (20-5(n-1))$

$b_n = (20-5(n-1))$

$b_{n+1} = (20-5(n+1-1)) = (20-5n)$

using the alternating series test;

$b_{n+1} \leq b_n$  for all n

$\lim_{n\rightarrow \infty} b_n = \lim_{n\rightarrow \infty} (20-5(n-1)) = -\infty$

⇒ the series diverges.

therefore, the given series i,e 20-15+10-5.... is divergent.