For Which of the Following Series Will the Ratio Test $\sum _ { n = 1 } ^ { \infty } \left( \frac { 99 } { 100 } \right) ^ { n }$

question 298

Multiple Choice

For which of the following series will the Ratio Test fail to give a definite answer (i.e., be inconclusive) ?
1) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 99 } { 100 } \right) ^ { n }$
2) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 100 } { 99 } \right) ^ { n }$
3) $\sum _ { n = 1 } ^ { \infty } n ^ { - 100 }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

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