Question

Rezolvați :
x+1/2+ x+2/3+ x+3/4+ ...+x+99/100=99

Answer 1

$\frac{x+1}{2}+ \frac{x+2}{3} + \frac{x+3}{4} +...+ \frac{x+99}{100}=99<=> \\ <=> (\frac{x+1}{2}-1) +(\frac{x+2}{3}-1)+ ( \frac{x+3}{4}-1)+...+( \frac{x+99}{100}-1)=0<=> \\ <=> \frac{x-1}{2}+ \frac{x-1}{3}+ \frac{x-1}{4}+... + \frac{x-1}{100}=0<=> \\ <=>(x-1)( \frac{1}{2}+ \frac{1}{3}+ \frac{1}{4}+ ...+ \frac{1}{100} )=0 \\ \\ \frac{1}{2}+ \frac{1}{3} + \frac{1}{4}+ ...+ \frac{1}{100} >0=>x-1=0=>x=1. \\ \\ Solutie:~x=1.$