QUIZ-If-the-sum-of-the-numbers-1-to-100-can-be-calculated-with-Carl-Gauss-s-method-then-How-do-we-calculate-the-sum-of-the-numbers-starting-from-2-and-going-up-to-100-by-twos-in-an-easy-way-with-the

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Question Number 186348 by test1234 last updated on 03/Feb/23

$$\mathrm{Q}UIZ:$$$$Ifthesumofthenumbers1to100can$$$$becalculatedwithCarl{Gauss}^{\prime }smethod,$$$$thenHowdowecalculatethesumofthe$$$$numbersstartingfrom2andgoingupto$$$$100bytwosinaneasywaywiththesame$$$$method?$$$$Or2+4+6+8+10+\dots +100=?$$

Commented by Frix last updated on 03/Feb/23

$$2+4+6+\dots +100=2\times (1+2+3+\dots +50)$$$$\mathrm{This}\mathrm{is}\mathrm{too}\mathrm{easy}$$

Commented by ajfour last updated on 04/Feb/23

$$1+2+3+\dots \dots \dots .+24+25$$$$50+49+48+\dots \dots \dots +27+26$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$$$51+51+51+\dots \dots \dots .+51+51$$$$=25\times 51=25(50+1)=1250+25$$

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