1. for what values of k the sequence (ssubn) will be monotone increasing and for what values of k it
will be monotone decreasing? Let ssubn =k and define ssub(n+1)= square root(4ssubn-1) for n is
a subset of N.
Solution
Since k is a natural number, hence, the following order relation is valid for all [k in N:]
[1 < 2 < ..... < k < k+1 < k+2 < ..... < n < n+1 < ...]
Based on the validity of statement above, the following statement is also valid:
[4 < 4*2 < ... < 4*k < 4(k+1) < ... < 4*n < 4(n+1) < ...]
Since 4>1 => 4 - 1 > 0 such that:
[4 - 1 < 4*2 - 1 <...< 4*k-1 < 4(k+1) - 1 <... < 4n-1<4(n+1)-1<...]
[sqrt(4-1)