MathDB

1.1

Part of 2020 Kyiv Mathematical Festival

Problems(1)

a_k = 1+/1/2 a_{k- 1} + 1/2 a_{k+1 }

Source: XIX Kyiv Mathematical Festival 2020 1.1

11/29/2020
(a) Find the numbers a0,...,a100a_0,. . . , a_{100}, such that a0=0,a100=1a_0 = 0, a_{100} = 1 and for all k=1,...,99k = 1,. . . , 99 : ak=12ak−1+12ak+1a_k = \frac12 a_{k- 1} + \frac12 a_{k+1 } (b) Find the numbers a0,...,a100a_0,. . . , a_{100}, such that a0=0,a100=1a_0 = 0, a_{100} = 1 and for all k=1,...,99k = 1,. . . , 99 : ak=1+12ak−1+12ak+1a_k = 1+\frac12 a_{k- 1} + \frac12 a_{k+1 }.
recurrence relationSequencealgebra