Question

Test the series for convergence or divergence. ∞ (−1)n 8n − 5 9n + 5 n...

Test the series for convergence or divergence.

∞ (−1)n
8n − 5
9n + 5
n = 1

Step 1

To decide whether

∞ (−1)n
8n − 5
9n + 5
n = 1

converges, we must find lim n → ∞

8n − 5
9n + 5

.

The highest power of n in the fraction is 1   

1

.

Step 2

Dividing numerator and denominator by n gives us lim n → ∞

8n − 5
9n + 5

= lim n → ∞

8 −
5
  
  +
5
n

.

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