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Sa se rezolve ecuatia 2x + 4x + 6x + ........ + 100x + 102 = x + 3x + 5x + ........ + 101x .

Răspuns :

2x + 4x + 6x + ........ + 100x + 102 = x + 3x + 5x + ........ + 101x .
2x*(1+2+3+...50)+102= x*(1+3+5+...101)
2x*50*51/2+102=x*51²
2550x+101=2601x
2550x-2601x= -102
-51x= -102
x=2

1+3+5+...101
an= 2n-1
101=2n-1
2n=101+1
n=51