Find the Sum of the Series $\sum _ { n = 1 } ^ { \infty } \frac { n } { ( \sqrt { n } + 1 ) }$

question 198

Multiple Choice

Find the sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { n } { ( \sqrt { n } + 1 ) }$ .

• A) \(\frac { 1 } { 5 }\)
• B) \(\frac { 1 } { 6 }\)
• C) \(\frac { 1 } { 2 }\)
• D) \(\frac { 1 } { 10 }\)
• E)1
• F) \(\frac { 3 } { 4 }\)
• G) \(\frac { 3 } { 2 }\)
• H)Divergent

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