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Can anyone help me with these?

• To: mathgroup@smc.vnet.net
• Subject: [mg10916] Can anyone help me with these?
• From: "Liam McAllister" <lmcallister@email.msn.com>
• Date: Thu, 12 Feb 1998 20:15:58 -0500

   1. The Binomial Coefficients
                         n
                           C
                            r
may be computed in Mathematica by typing Binomial[n,r]. Apart from the
fact that nC0=nCn=1 for all positive integers n, there are equalities
like 4C2=6C1=6 which make it rather difficult to work out how many
different numbers occur as binaomial coefficients nCr as n ranges from
1 to N (say) and r ranges from 0 to n. Write a function h[] which will
compute this number. Then use ListPlot[] (with PlotJoined->True) to
compare N with h[N] as N ranges from 1 to 20.
*************************************************** 2. Produce complete
and accurate graphs of the functions defined by the formulae
 f(x)=cos(cos(2 Pi x)) and  g(x)=cos(sin(2 Pi x)) on the interval [0,12]
*************************************************** 3. Write a function
d in Mathematica such that d(n) is the fraction of the first n
Fibonnaci numbers which are prime. Find d(100). Use ListPlot[ ] with
(PlotJoined->true) to give a graphical representation of the way d(n)
varies with n for n =10, 20, ..., 100. Ensure that the viewer can see
clearly where in the interval [0,1] d(n) lies.
Fionnaci is f1=f2=1 and fn=fn-1 + fn-2 for n>2


Thanks in advance,

Liam.