#1
FP1 induction example

Prove f(n) is divisible by 576 for n=1,2,3,4.....

f(1)=576

If (for some k >1) f(k) is divisible by 576 then for some natural number m.

etc..

An interesting problem http://www.thestudentroom.co.uk/show....php?t=1293042

____________________

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C=...
S=...

If w is a cube root of 1 then theta=0, 2pi/3, 4pi/3

(1-w)^6 = -27, 0, 27
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Step 1 2010 Q13

P(first text in second hour) = P(0 in first hour)*P(>0 in second hour)

gives the required equation

For the two positive values of lambda.. one is easy, for the other show that for 0<p<1/4

Starting with leads to so and so

Mildred's lamdas satisfy

so using product of roots

The combined rate for the two phones is subbing this in for lambda in the given equation results in p(1-p) as the required probability.
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