MathDB

Let \{k_n\}_{n \equal{} 1}^{\infty} be a sequence of real numbers having the properties

k_1 > 1

and k_1 \plus{} k_2 \plus{} \cdots \plus{} k_n < 2k_n for n \equal{} 1,2,.... Prove that there exists a number

q > 1

such that

k_n > q^n

for every positive integer

n

Problem Statement