Question Number 134668 by EDWIN88 last updated on 06/Mar/21
![1+1+4−6−8−10+12+14+16−18−20−22+... S_(900) = ?](https://www.tinkutara.com/question/Q134668.png)
$$\mathrm{1}+\mathrm{1}+\mathrm{4}−\mathrm{6}−\mathrm{8}−\mathrm{10}+\mathrm{12}+\mathrm{14}+\mathrm{16}−\mathrm{18}−\mathrm{20}−\mathrm{22}+… \\ $$$$\mathrm{S}_{\mathrm{900}} \:=\:? \\ $$
Answered by benjo_mathlover last updated on 06/Mar/21
![⇒1+1+4_(6) −6−8−10_(−24) +12+14+16_(42) −18−20−22_(−60) +...= ⇒6−24+42−60+..._(300 factor) = ⇒−18−18−18−..._(150 times) = −18×150 = −2700](https://www.tinkutara.com/question/Q134669.png)
$$\Rightarrow\underset{\mathrm{6}} {\underbrace{\mathrm{1}+\mathrm{1}+\mathrm{4}}}\:\underset{−\mathrm{24}} {\underbrace{−\mathrm{6}−\mathrm{8}−\mathrm{10}}}\:\underset{\mathrm{42}} {\underbrace{+\mathrm{12}+\mathrm{14}+\mathrm{16}}}\:\underset{−\mathrm{60}} {\underbrace{−\mathrm{18}−\mathrm{20}−\mathrm{22}}}\:+…= \\ $$$$\Rightarrow\underset{\mathrm{300}\:\mathrm{factor}} {\underbrace{\mathrm{6}−\mathrm{24}+\mathrm{42}−\mathrm{60}+…}}\:= \\ $$$$\Rightarrow\underset{\mathrm{150}\:\mathrm{times}} {\underbrace{−\mathrm{18}−\mathrm{18}−\mathrm{18}−…}}\:=\:−\mathrm{18}×\mathrm{150}\:=\:−\mathrm{2700} \\ $$$$ \\ $$