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x+(x+1)/2 +(x+2)/3 +...+(x+99)/100=100

Răspuns :

x-1+1+(x-1+2)/2+(x-1+3)/3+.....+(x-1+100)/2=100
(x-1)+1+(x-1)/2+1+(x-1)/3+1+....+(x-1)/100+1=100
(x-1)(1+1/2+1/3+.....1/100)+100=100
(x-1)(1+1/2+1/3+....+1/100)=0
x-1=0, x=1