Determine If the Series Converges or Diverges $$\sum _ { n = 1 } ^ { \infty } \left( \frac { 1 } { n ^ { 3 / 2 } } - \frac { 1 } { ( n + 1 ) ^ { 3 / 2 } } \right)$$

question 43

Multiple Choice

Determine if the series converges or diverges. If the series converges, find its sum.
- $$\sum _ { n = 1 } ^ { \infty } \left( \frac { 1 } { n ^ { 3 / 2 } } - \frac { 1 } { ( n + 1 ) ^ { 3 / 2 } } \right)$$

• A) converges; \(\frac { 1 } { 3 \sqrt { 3 } }\)
• B) diverges
• C) converges; 1
• D) converges; \(\frac { 1 } { 6 \sqrt { 6 } }\)

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