Question

43+44+45+...+202
5+10+15+...+200
1+7+13+...+211​

Answer 1

Răspuns:

formula lui Gauss:

n=(u-p):r+1

S=(u+p)×n:2

ratia (r) se afla scazand termenii:

Exemplu:

43+44+45+...+202

r=44-43; r=1

r= 45-44; r=1

Deci, ratia este 1

Aflam numarul de numere (n):

43+44+45+...+202

n= (202-43):1+1

n=159:1+1

n=159+1

n=160

Acum aflam suma (S)

S=(202+43)×160:2

S= 245×160:2

S=245×80

S=19600

______________________

La acest exercitiu procedam la fel:

5+10+15+...+200

ratia este de 5, deoarece 10-5=5, 15-10=5

n=(200-5):5+1

n=195:5+1

n=39+1

n=40

S=(200+5)×40:2

S=205×40:2

S=205×20

S= 4100

________________________

1+7+13+...+211

r= 7-1; r=6

n=(211-1):6+1; n=210:6+1; n=35+1; n=36

S= (211+1)×36:2; S=212×36:2; S=18×212; S=3816