Find the 51st term of the arithmetic sequence 29,9,−11,...
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm using a photocopier to reduce an image over and over by 50%, so the exponential function
models the new image size, where x is the number of reductions.
Let be two real numbers such that . For , we define and
a) Prove that the sequence is monotonically increasing and that the sequence is monotonically decreasing.
b) Show that the sequences and are bounded.
c) Deduce that the two sequences converge and prove that they converge to the same limit.