Question

Please Help! sigma limit see equation in note below

Answer 1

\[\lim_{n \rightarrow \infty} \frac{ 1 }{ n} [(\frac{ i }{ n })^3 +1] \]

Answer 2

sorry should have put sigma with i=1 on bottom and n on top

Answer 3

\[\lim_{n \rightarrow \infty} \sum_{I=1}^{n} \frac{ 1 }{ n} [(\frac{ i }{ n })^3 +1] \]

Answer 4

\[\lim_{n \rightarrow \infty} \sum_{i=1}^{n} (i/n)^{3} + 1\]

Answer 5

Okay I got the question....

Answer 6

I am way lost on this

Answer 7

\[1/n [ i ^{3}/n ^{3} + 1] = 1/n [ (i ^{3} + n^{3}) / n^{3} ] = 1/n^{4} [ i^{3} + n^{3} ] \]
Now apply sigma...n is a constant, so bring 1/n^4 out of sigma

Answer 8

\[\sum_{i=1}^{n}i^{3} + \sum_{i=1}^{n}n^{3} \]
\[= n^{2}(n+1)^{2} / 4 + (n \times n^{3})\]
\[= (5n^{4} + 2n^{3} + n^{2}) / 4 \]

Answer 9

\[\lim_{n \rightarrow \infty} (5n^{4} + 2n^{3} + n^{2}) / 4n^{4}\]
\[= \lim_{n \rightarrow \infty} n^{4}(5 + 2/n + 1/n^{2}) / 4n^{4}\]
\[= \lim_{n \rightarrow \infty} 5/4 + 2/4n + 1/4n^{2}\]
\[= 5/4 + 0 + 0 = 5/4\]

Answer 10

Oh great!! I spent a lot of time solving and typing this just to see that you are offline..! That is satisfying