Quote (Beat @ Nov 30 2014 02:27pm)
let C0, C1, C2 .... be defined by the formulaCn= 2^n - 1 for all
integers n >(or equal to) 0. Show that this sequence satisfies the recurrence relation Ck= 2C(k-1)+ 1
Quote (Beat @ Nov 30 2014 02:31pm)
solution they give you
subsitute k and k-1 in place of n
Ck = 2^k -1
C(k-1) = 2^(k-1) -1
for all int k >(or equal to) 0
2Ck-1 + 1 = 2(2^(k-1) -1
=2^k -2 + 1
=2^k -1
=Ck
Bolded part is what I dont get
it says it was substituted from C(k-1) = 2^(k-1) -1
so was the 2 and the +1 just added so the right side would equal ck?