$//$ Assume i$,$ j$,$ k$,$ n are integers

for i $=1$ to n do

for j $=1$ to i $\{$

k $=1$;

while $($k $<$ i$)\{$

perform ;

k $=2*$k;

$\}$

$\}$

Find an expression $($as a summation$)$ for f$($n$),$ the number of times

is performed when the algorithm is executed. Show your intermediate steps.