1-1-4-6-8-10-12-14-16-18-20-22-S-900-

Question Number 134668 by EDWIN88 last updated on 06/Mar/21

1 + 1 + 4 - 6 - 8 - 10 + 12 + 14 + 16 - 18 - 20 - 22 + \dots

S_{900} = ?

Answered by benjo_mathlover last updated on 06/Mar/21

\Rightarrow \underset{6}{\underset{⏟}{1 + 1 + 4}} \underset{- 24}{\underset{⏟}{- 6 - 8 - 10}} \underset{42}{\underset{⏟}{+ 12 + 14 + 16}} \underset{- 60}{\underset{⏟}{- 18 - 20 - 22}} + \dots =

\Rightarrow \underset{300 factor}{\underset{⏟}{6 - 24 + 42 - 60 + \dots}} =

\Rightarrow \underset{150 times}{\underset{⏟}{- 18 - 18 - 18 - \dots}} = - 18 \times 150 = - 2700