$($h$)$ Use the formula for geometric series:

nX

k$=0$

rk $=$

$($

t $+1$ if r $=1$

rt$+11$

r$1$ else

to evaluate the sum from the previous question.

$($i$)$ If a

bd $=1,$ what is the big$-$O runtime of the algorithm? You should assume a$,$ b$,$ and d are

constants, and n is the variable that gets large.

$($j$)$ If a

bd $<1,$ what is the big$-$O runtime of the algorithm? You should assume a$,$ b$,$ and d are

constants, and n is the variable that gets large.

$($k$)$ If a

bd $>1,$ what is the big$-$O runtime of the algorithm? You should assume a$,$ b$,$ and d are

constants, and n is the variable that gets large.