Question

suma lui gauss
cum se face
1+2+3+.....+54=
1+2+3+......+13=
4+5+6+7+.......+200=
11+12+13+........+97=
32+33+34+......+112=

Answer 1

1+2+3+…..+54
formula [(primul+ultimul) x nr de termeni] :2
(1+54) x 54 : 2
55 x 54 : 2
1485

1+2+3+…+13
(1+13) x 13 :2
14 x 13 :2
7 x 13
=91


4+5+6+…+200
intai aflam nr de termeni dupa formula
(ultimul-primul) : rație +1
unde ratia este diferenta dintre 2 termeni consecutivi
(200-4):1 +1
196+1
=197

(4+200) x 197 :2
204 : 2 x 197
20,094


11+12+13+…+97
nr termeni= (97-11):1 +1
86+1
87
(11+97) x 87 : 2
108 : 2 x 87
54 x 87
=4698


32+33+34+…+112
nr termeni= (112-32):1 +1
80 +1
81

(32+112) x 81 :2
144 : 2 x 81
72 x 81
5832