Answer:
Option b is correct.
The series 20-15+10-5....is Divergent
Step-by-step explanation:
Alternating series Test:
[tex]\sum_{n=1}^{\infty} (-1)^{n-1} (b_n) =b_1-b_2+b_3-........[/tex]
[tex]b_n>0[/tex] satisfies:
- [tex]b_{n+1} \leq b_n[/tex] for all n
- [tex]\lim_{n\rightarrow \infty} b_n = 0[/tex]
Then the series converges,
otherwise diverges.
Given the series: 20-15+10-5....
This is a alternating series:
[tex]\sum_{n=1}^{\infty} (-1)^{n-1} (20-5(n-1))[/tex]
[tex]b_n = (20-5(n-1))[/tex]
[tex]b_{n+1} = (20-5(n+1-1)) = (20-5n)[/tex]
using the alternating series test;
[tex]b_{n+1} \leq b_n[/tex] for all n
[tex]\lim_{n\rightarrow \infty} b_n = \lim_{n\rightarrow \infty} (20-5(n-1)) = -\infty[/tex]
⇒ the series diverges.
therefore, the given series i,e 20-15+10-5.... is divergent.
