Question Number 134668 by EDWIN88 last updated on 06/Mar/21
$$\mathrm{1}+\mathrm{1}+\mathrm{4}−\mathrm{6}−\mathrm{8}−\mathrm{10}+\mathrm{12}+\mathrm{14}+\mathrm{16}−\mathrm{18}−\mathrm{20}−\mathrm{22}+... \\ $$$$\mathrm{S}_{\mathrm{900}} \:=\:? \\ $$
Answered by benjo_mathlover last updated on 06/Mar/21
$$\Rightarrow\underset{\mathrm{6}} {\underbrace{\mathrm{1}+\mathrm{1}+\mathrm{4}}}\:\underset{−\mathrm{24}} {\underbrace{−\mathrm{6}−\mathrm{8}−\mathrm{10}}}\:\underset{\mathrm{42}} {\underbrace{+\mathrm{12}+\mathrm{14}+\mathrm{16}}}\:\underset{−\mathrm{60}} {\underbrace{−\mathrm{18}−\mathrm{20}−\mathrm{22}}}\:+...= \\ $$$$\Rightarrow\underset{\mathrm{300}\:\mathrm{factor}} {\underbrace{\mathrm{6}−\mathrm{24}+\mathrm{42}−\mathrm{60}+...}}\:= \\ $$$$\Rightarrow\underset{\mathrm{150}\:\mathrm{times}} {\underbrace{−\mathrm{18}−\mathrm{18}−\mathrm{18}−...}}\:=\:−\mathrm{18}×\mathrm{150}\:=\:−\mathrm{2700} \\ $$$$ \\ $$