LIMITS!

[Guest]

lim (3/n)
n-> (infinite)


find the limit by using properities of limits

 

[stapel]

find the limit by using properities of limits

What "properties" have you been given? For instance, have you been given any rules regarding the limit of 1/n as n gets arbitrarily large ("goes to infinity")?

Thank you.

Eliz.

 

[Guest]

nevermind i figured it out

but here's another question

find the limit of the sequence of decimals formed by an increasing number of 3s: .3, .33, .333, .3333, .33333......

 

[soroban]

Hello, alohagrlxo!

Find the limit of the sequence of decimals formed by an increasing number of 3s:
\(\displaystyle \;\;\;0.3,\;0.33,\;0.333,\;0.3333,\;0.33333,\;\cdots\)

The number is of the form: \(\displaystyle \,S\;=\;\frac{3}{10}\,+\,\frac{3}{10^2}\,+\,\frac{3}{10^3} \,+\,\frac{3}{10^4}\,+\,\cdots\)

This is an infinite geometric series with first term \(\displaystyle a=\frac{3}{10}\) and common ratio \(\displaystyle r = \frac{1}{10}\)

The sum is: \(\displaystyle \L\,S\;=\;\frac{\frac{3}{10}}{1\,-\,\frac{1}{10}} \;=\;\frac{\frac{30}{10}}{\frac{9}{10}}\;=\;\frac{1}{3}\)

 

[stapel]

here's another question

In the future, please post new questions as new threads, not as replies to old threads, where they are frequently over-looked. Thank you.

find the limit of the sequence of decimals formed by an increasing number of 3s: .3, .33, .333, .3333, .33333......

Hint: Consider geometric series.

Eliz.