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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)  = ?

$$\mathrm{1}+\mathrm{1}+\mathrm{4}−\mathrm{6}−\mathrm{8}−\mathrm{10}+\mathrm{12}+\mathrm{14}+\mathrm{16}−\mathrm{18}−\mathrm{20}−\mathrm{22}+... \\ $$$$\mathrm{S}_{\mathrm{900}} \:=\:? \\ $$

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

$$\Rightarrow\underset{\mathrm{6}} {\underbrace{\mathrm{1}+\mathrm{1}+\mathrm{4}}}\:\underset{−\mathrm{24}} {\underbrace{−\mathrm{6}−\mathrm{8}−\mathrm{10}}}\:\underset{\mathrm{42}} {\underbrace{+\mathrm{12}+\mathrm{14}+\mathrm{16}}}\:\underset{−\mathrm{60}} {\underbrace{−\mathrm{18}−\mathrm{20}−\mathrm{22}}}\:+...= \\ $$$$\Rightarrow\underset{\mathrm{300}\:\mathrm{factor}} {\underbrace{\mathrm{6}−\mathrm{24}+\mathrm{42}−\mathrm{60}+...}}\:= \\ $$$$\Rightarrow\underset{\mathrm{150}\:\mathrm{times}} {\underbrace{−\mathrm{18}−\mathrm{18}−\mathrm{18}−...}}\:=\:−\mathrm{18}×\mathrm{150}\:=\:−\mathrm{2700} \\ $$$$ \\ $$

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