MathDB

2

Part of 2008 South East Mathematical Olympiad

Problems(2)

find general term formula for sequence

Source: China south east mathematical olympiad 2008 day1 problem 2

7/14/2013
Let {an}\{a_n\} be a sequence satisfying: a1=1a_1=1 and an+1=2an+n⋅(1+2n),(n=1,2,3,⋯ )a_{n+1}=2a_n+n\cdot (1+2^n),(n=1,2,3,\cdots). Determine the general term formula of {an}\{a_n\}.
algebra unsolvedalgebra
three points are collinear

Source: China south east mathematical Olympiad 2008 day2 problem 6

7/15/2013
Circle II is the incircle of △ABC\triangle ABC. Circle II is tangent to sides BCBC and ACAC at M,NM,N respectively. E,FE,F are midpoints of sides ABAB and ACAC respectively. Lines EF,BIEF, BI intersect at DD. Show that M,N,DM,N,D are collinear.
geometrytrigonometrygeometry unsolved