Question

Rezolva ecuatia x+2x+3x...+100x=50500

Answer 1

pentru x+2x+3x...+100x folosim suma lui Gauss:

s= n(n+1)/2
s= 100x(100x+1)/2
s= 100x•101x/2
s= 10100x/2
s= 5050x

5050x= 50500
x= 50500/5050
x= 10

Answer 2

x + 2 x + 3 x + ...... + 100 x = 50 500

x × ( 1 + 2 + 3 + .... + 100 ) = 50 500

x → factor comun

1 + 2 + 3 + ..... + 100 = 100 × 101 : 2 = 50 × 101 = 5 050

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X × 5 050 = 50 500

X = 50 500 : 5 050

X = 10