Use the result of Exercise 25 to evaluate What can be said

Chapter , Problem 26AAE

(choose chapter or problem)

Use the result of Exercise 25 to evaluate

a. \(\lim _{n \rightarrow \infty} \frac{1}{n^{2}}(2+4+6+\ldots+2 n)\),

b. \(\lim _{n \rightarrow \infty} \frac{1}{n^{16}}\left(1^{15}+2^{15}+3^{15}+\ldots+n^{15}\right)\),  

c. \(\lim _{n \rightarrow \infty} \frac{1}{n}\left(\sin \frac{\pi}{n}+\sin \frac{2 \pi}{n}+\sin \frac{3 \pi}{n}+\ldots+\sin \frac{n \pi}{n}\right)\).

What can be said about the following limits?

e. \(\lim _{n \rightarrow \infty} \frac{1}{n^{17}}\left(1^{15}+2^{15}+3^{15}+\ldots+n^{15}\right)\)

f. \(\lim _{n \rightarrow \infty} \frac{1}{n^{15}}\left(1^{15}+2^{15}+3^{15}+\ldots+n^{15}\right)\)

Equation Transcription:

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Text Transcription:

lim_n right arrow infinity 1/n^(2+2+4+6+...+2n)

lim_n right arrow infinity 1/n^16(1^15+2^15+ 3^15+...+n^15)

lim_n right arrow infinity 1/n (sin pi/n+sin 2pi/n + sin 3pi/n +...+sin npi/n)

lim_n right arrow infinity 1/n^17(1^15 + 2^15 + 3^15 +...+n^15)

lim_n right arrow infinity 1/n^15 (1^15 + 2^15 + 3^15+...+n^15)