The ith term of the series (i starts at 0) is . The series ends when we hit T(1), or .

T(n) = n + n + n + ... +

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

=
+ nT(1)

= nlgn + n

= nlgn +

= nlgn +

=

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