Solution Found!
?Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined
Chapter 4, Problem 86(choose chapter or problem)
Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0,1].
\(\lim _{n \rightarrow \infty} \frac{1}{n}\left(\sqrt{\frac{1}{n}}+\sqrt{\frac{2}{n}}+\sqrt{\frac{3}{n}}+\cdots+\sqrt{\frac{n}{n}}\right)\)
Equation Transcription:
Text Transcription:
lim _{n rightarrow infty}frac{1}{n}(sqrt{\frac{1}{n}} + sqrt{frac{2}{n}} + sqrt{frac{3}{n}} + cdots + sqrt{frac{n}{n}})
Questions & Answers
QUESTION:
Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0,1].
\(\lim _{n \rightarrow \infty} \frac{1}{n}\left(\sqrt{\frac{1}{n}}+\sqrt{\frac{2}{n}}+\sqrt{\frac{3}{n}}+\cdots+\sqrt{\frac{n}{n}}\right)\)
Equation Transcription:
Text Transcription:
lim _{n rightarrow infty}frac{1}{n}(sqrt{\frac{1}{n}} + sqrt{frac{2}{n}} + sqrt{frac{3}{n}} + cdots + sqrt{frac{n}{n}})
ANSWER:
Step 1 of 3
We can rewrite the expression as follows
