sorry i don't really understand that - how did you work out that s was 5/6? And did you just choose random values for a0, a1 and an? I have rechecked my homework question and that is exactly what it said!
1. Homework Statement
Let s be the sum of the alternating series \sum(from n=1 to \infty)(-1)n+1an with n-th partial sum sn. Show that |s - sn| \leqan+1
2. Homework Equations
I know about Cauchy sequences, the Ratio test, the Root test
3. The Attempt at a Solution
I really have...
Right okay, so now for the variance do I use the same formula but use 1.6 (I presume it was just a typo and it should have been 0.7 *2) instead of 0.53?
Do I then use the Central Limit Theorem for part b?
Okay I have since realised that for part a) I think i was doing it wrong so now for the mean I have:
((0.7*2) + (0.2*1) + (0.1*0))/3 = 0.53
But for the Variance I have:
((0.7 - 0.53)2+ (0.2 - 0.53)2 + (0.1 - 0.53)2)/3 = 0.1076 which makes far more sense!!
Now I'm thinking of using...
1. Homework Statement
Suppose that, on average, 70% of graduating students want 2 guest tickets for a graduation ceremony, 20% want 1 guest ticket and the remaining10% don't want any guest tickets.
(a) Let X be the number of tickets required by a randomly chosen student. Find the mean and...
The answer to part a) is correct, however, I don't really understand what calculation you've done for part b).
Personally I would just use the Choose function i.e. 12C3 * 0.0301^3 * 0.9699^9
1. Homework Statement
Suppose that f: R -> R is continuous on R and that lim (x -> \infty+)(f(x) = 0) and lim (x -> \infty-)(f(x)=0).
Prove that f is bounded on R
2. Homework Equations
I have got the proof of when f is continuous on [a,b] then f is bounded on[a,b] but I'm unsure as to...
1. Homework Statement
Let V = {differentiable f:R -> R}, a vector space over R. Take g1,g2,g3 in V where g1(x) = e^{}x, g2(x) = e^{}2x and g3(x) = e^{}3x.
Show that g1, g2 and g3 are distinct.
2. Homework Equations
If g1-g3 are linearly independent, it means that for any constant, k in F...
1. Homework Statement
Prove that lim n \rightarrow\infty 2^{}n/n! = 0
2. Homework Equations
This implies that 2^{}n/n! is a null sequence and so therefore this must hold:
(\forall E >0)(\existsN E N^{}+)(\foralln E N^{}+)[(n > N) \Rightarrow (|a_{}n| < E)
3. The Attempt at a...