Question

A=1+2+3+.............+2013
B=108+109+110+............+149
C=13+14+15+..........+42
a-(b-c)=

Answer 1

a = 1 + 2 + 3 + ............. + 2 013

a = 2013 x ( 1 + 2013 ) / 2

a = 2013 x 1007

a = 2 027 091

___________________

b = 108 + 109 + 110 + ............ + 149

→ stabilim cati termeni are suma cu ratia 1 ( 109 - 108 = 1 )

( 149 - 108 ) + 1 = 41 + 1 = 42 termeni are suma

b = 42 x ( 108 + 149 ) / 2

b = 21 x 257

b = 5 397

________________

c = 13 + 14 + 15 + .......... + 42

→ stabilim cati termeni are suma

42 - 13 + 1 = 29 + 1 = 30 termeni are suma

c = 30 x ( 13 + 42 ) / 2

c = 15 x 55

c = 825

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a - ( b - c ) = 2 027 091 - ( 5 397 - 825 ) = 2 027 091 - 4 572 = 2 022 519