evaluate-the-limit-by-interpreting-it-as-a-riemann-sum-and-then-computing-the-co

Question

Evaluate the limit by interpreting it as a Riemann sum and then computing the corresponding integral.lim⁡n→∞∑k=1n1nln⁡(1+2kn)

\displaystyle \lim_{n	o\infty}\sum_{k=1}^n\frac{1}{n}\ln\left(1+\frac{2k}{n}ight)

Accepted Answer

32ln⁡3−1\displaystyle\frac{3}{2}\ln{3}-1

Answer

52ln⁡2−1\displaystyle\frac{5}{2}\ln{2}-1

Answer

32ln⁡3+1\displaystyle\frac{3}{2}\ln{3}+1

Answer

52ln⁡2+1\displaystyle\frac{5}{2}\ln{2}+1

Evaluate the limit by interpreting it as a Riemann sum and then computing the corresponding integral.limn→∞∑k=1n1nln(1+2kn) \(\displaystyle\) \(\lim\)_{n\(\to\[\infty\)}\(\sum\)_{k=1}^n\(\frac{1}{n}\]\ln\[\left\)(1+\(\frac{2k}{n}\]\right\))