Question

S=1+2+3+......+10;S=2+4+6+......+20;S=1+2+3+....+2019;S=2+4+6+....+2020;S=5+10+15+.....+35;S=11+12+13+.....+78; calculați ​

Answer 1

1)= S= cu Suma lui Gauss

= 10×11/2 = 5×11= 55

2) S= scoatem factori comun (2)

S= 2×(1+2+3+.....+10)

S= 2×10×11/2= 10×11=

= 110

3)= 2019 ×2020/2= 2019×1010=
= 2039190

4)= scoatem factori comun (2)

= 2×(1+2+3+......+1010)

S= 2 × 1010×1011/2=

= 1010×1011= 1021110
Sau
1010×(1010+1) = 1010² +1010

5)= scoatem factori comun (5)

S= 5×(1+2+3+......+7)

= 5× 7×8 /2 = 5×7×4= 140

6)=
78×79/2 − 10×11/2=

= 39× 79 − 5×11 =

= 3081 − 55= 3026