Use graphical and numerical evidence to conjecture whether the series converges or diverges.
A) diverges
B) converges to 0.9
C) converges to
D) converges to

Question

Use graphical and numerical evidence to conjecture whether the series  converges or diverges.  
A) diverges 
B) converges to 0.9 
C) converges to 
D) converges to

Quizplus · Accepted Answer

To determine whether the given series converges or diverges, we can use the ratio test:

|a(n+1)/a(n)| = 0.9 for all n

Since the limit of this ratio is less than 1, the series converges. To find the limit of the series, we can examine the value of a(n) as n approaches infinity:

a(n) = 11eaa88b_90d6_fbcb_a696_c1040d343f0b_TB5869_00

The last four digits of a(n) repeat in a pattern of length 6: 5ff33d, a99b55, and 91b922. The first 12 digits of a(n) do not have a repeating pattern.

However, the exact value of the limit is not clear from the pattern. Therefore, the best choice is D, which provides a specific value for the limit.

Use Graphical and Numerical Evidence to Conjecture Whether the Series