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

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

Answered by benjo_mathlover last updated on 06/Mar/21

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

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