Question

[Do Gia Bach]

1,25 - 2,75 + 4,25 - 5.75 + ... + 25,25

Answer 1

[Kudo Shinichi]

                                   Số các số hạng là : 

                                     \(\left(25,25-1,25\right):1,5+1=17\)

                                Tổng dãy số trên là :

                                \(\left(25,25+1,25\right).17:2=225,25\)

                   Chúc bạn học tốt !!!

Answer 2

[.]

Ta có:1,25 - 2,75 + 4,25 - 5.75 + ... + 25,25

      =>\(\frac{5}{4}-\frac{11}{4}+\frac{17}{4}-\frac{23}{4}+...+\frac{101}{4}\)

      =>\(\frac{5}{4}+\frac{17}{4}+....+\frac{101}{4}-\frac{11}{4}-\frac{23}{4}-....-\frac{95}{4}\)

      =>\(\left(\frac{5}{4}+\frac{17}{4}+...+\frac{101}{4}\right)-\left(\frac{11}{4}+\frac{23}{4}+....+\frac{95}{4}\right)\)

      =>\(\left(\frac{5+17+...+101}{4}\right)-\left(\frac{11+23+....+95}{4}\right)\)

      =>\(\left(\frac{\left(101+5\right).\left[\left(101-5\right):12+1\right]:2}{4}\right)-\left(\frac{\left(95+11\right).\left[\left(95-11\right):12+1\right]:2}{4}\right)\)

      =>\(\left(\frac{106.\left(96:12+1\right):2}{4}\right)-\left(\frac{106.\left(84:12+1\right):2}{4}\right)\)

      =>\(\left(\frac{53.\left(8+1\right)}{4}\right)-\left(\frac{53.\left(7+1\right)}{4}\right)\)

     =>\(\left(\frac{53.9}{4}\right)-\left(\frac{53.8}{4}\right)\)

     =>\(\frac{477}{4}-\frac{424}{4}=\frac{53}{4}=13,25\)

Vậy 1,25 - 2,75 + 4,25 - 5.75 + ... + 25,25 = 13,25

Chúc bn học tốt!