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Examination sample, of the mentioned university
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Problem SolvingSet 21
24 July 2012
1. (a) A sequence x1, x2, . . . of real numbers satises
xn+1 = xn cosxn
for all n 1. Does it follow that this sequence con-verges for all initial values x1?
(b) A sequence y1, y2, . . . of real numbers satises
yn+1 = yn sin yn
for all n 1. Does it follow that this sequence con-verges for all initial values y1?
2. Show that in any collection of 52 distinct positive integersthere are two distinct numbers whose sum or difference isdivisible by 100.
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