This question is really important
Prove or disprove that
lim_(n→∞) ((3^n m+3^(n−1) )/2^(⌈(n/2)⌉) ) + (3^(n−1) /2^n )
the limit exists for m ∈ N \B
where B = {n ∣ log_2 (n) ∈ N }
How many ways to arrnge
the letters ABCCCDEFG
(1) in general .
(2) all 3 Cs must be together
(3) only 2 Cs must be together
(4) no 2 or 3 Cs be together
(5) no letter still in its
original place .
Find all two-digit numbers that are equal to four times the sum
of their digits. Solve this using at least two different methods
and verify your answers.