The ith term of the series (i starts at 0) is
2^{i} *T*(*n*/2^{i}).
The series ends when we hit T(1), or
.

T(n) = n + n + n + ... +
2^{lg n} *T*(1)

= n + n + n + ... + nT(1)

=
+ nT(1)

= nlgn + n

= nlgn +

= nlgn + *o*(*nlgn*)

=

Do not simplify asymptotic expressions until there is no summation in the
expression.