apparently every computer program gives me an error finding the limit of this:
$\displaystyle [\frac{4n+1}{n^2}+(\frac{1}{5})^n * \frac{n}{2n+1} + (1+\frac{10}{n})^{3n}$
my result is $\displaystyle e^{1000}$. looks way too strange for me
apparently every computer program gives me an error finding the limit of this:
$\displaystyle [\frac{4n+1}{n^2}+(\frac{1}{5})^n * \frac{n}{2n+1} + (1+\frac{10}{n})^{3n}$
my result is $\displaystyle e^{1000}$. looks way too strange for me
The sequence is the sum of three sequences...
a) $\displaystyle \frac {1+4n}{n^2}$ for which is $\displaystyle \lim_{n\rightarrow \infty} =0$
b) $\displaystyle (\frac {1}{5})^{n}\cdot \frac{n}{1+2n}$ for which is $\displaystyle \lim_{n\rightarrow \infty} =0$
c) $\displaystyle (1+\frac {10}{n})^{3n}$ for which is $\displaystyle \lim_{n\rightarrow \infty} (1+\frac {30}{3n})^{3n}= e^{30}$
... so that the whole limit is $\displaystyle e^{30}$ ...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$
hm that c part is a bit unclear for me
i thought i could write $\displaystyle \lim(1+\frac{10}{n})^{3n} = \lim (1+\frac{10}{n})^n*\lim (1+\frac{10}{n})^n*\lim (1+\frac{10}{n})^n$
oh damn.... i did a really embarassing mistake basic algebra here i come again... $\displaystyle e^{10}*e^{10}*e^{10} = e^{30}$ and not to the power of 1000...
but thanks, needed to clarify if my thinking was right