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Question

Question: If \(\lim _ { n \rightarrow \infty } S _ { n }\) is equal to...

If lim⁡n→∞Sn\lim _ { n \rightarrow \infty } S _ { n } is equal to

A

log 2

B

2 log 2

C

3log⁡23 \log 2

D

4 log 2

Answer

2 log 2

Explanation

Solution

∴ lim⁡n→∞Sn=∫011x(1+x)dx\lim _ { n \rightarrow \infty } S _ { n } = \int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt { x } ( 1 + \sqrt { x } ) } d x

= 2[log⁡(1+x)]01=2log⁡22 [ \log ( 1 + \sqrt { x } ) ] _ { 0 } ^ { 1 } = 2 \log 2