Wow. That's creative. So basically I can't just say that n^3 > 3n^2 + 3n + 1 because 3n^2 isn't the only term? And is there a reason your last inequality is 10n^2 <= n^3 instead of just 10n^2 < n^3? Can I just say 10n^2 <n^3 because n>=10?
Thank you!
Homework Statement
Using the principle of mathematical induction, prove that for all n>=10, 2^n>n^3
Homework Equations
2^(n+1) = 2(2^n)
(n+1)^3 = n^3 + 3n^2 + 3n +1
The Attempt at a Solution
i) (Base case) Statement is true for n=10
ii)(inductive step) Suppose 2^n > n^3 for some integer >=...
Hello everyone. I am a little confused as to how I should organize if else statements in java. Here is an example from my Leap Year program:
if (x<1600) {
System.out.println(setError);
} else if (x>2013) {
System.out.println(setError);
} else {
if...
Mhmm. What do you use VB.NET for? I took an elective called Visual Basic, in which, we created simple programs like a calculator for example. How does this connect to html and web development?
That makes sense. My friend said he just uses notepad, which I guess, means pure HTML code. So I should learn HTML5, or learn HTML4 first? I think html5 is a work in progress but my friend told me that everyone is using it these days.
Thanks for your reply. I don't think I will be "designing" that much. My friend said that he mostly codes and debugs. I took a web design elective in high school and got my feet wet in Dreamweaver cs5. We dealt very little with the actual html code behind it though.
I'm going to be in school for a while and I need some source of income. My friend has a friend who finds jobs for him that have to do with web development. He says that I could do the same if I just learned HTML5 and gain some experience with the Adobe Suite. How hard is to learn these?
Ah, that was the limit of natural log of the sequence. Since ln(a sub n) = 0, (a sub n) = e^0=1. Thank you so much for guiding me through this. I feel so much better.
by the way, is there an easier way to write (a sub n)?...I'm new to this.
I am not getting the right answer. (ln(3/n))/n: the derivative of the numerator is (-1/n) and the derivative of the denominator is 1. Which gives me lim = 0. Did I differentiate correctly?
I am sorry "I Like Serena", I don't understand what you mean by "n1/n could approach anything from 1 up". What ever value n has, you will be taking it to the power of 0. So it has to approach 1. I know I am wrong but I don't understand how.
Thank you,
So I get (3^(1/n)) / (n^(1/n))
If n approaches ∞, the the numerator is 1 because the exponent approaches 0.
So would it be sufficient for me to apply the same mentality to denominator and say
that it approaches 1? That would give me 1 for the limit of the sequence which is the...