Răspunsuri

2014-10-26T12:17:11+02:00
 \frac{1}{1*2}+ \frac{1}{2*3}+ \frac{1}{3*4}+...+ \frac{1}{49*50}
scriem :  \frac{1}{1*2} =  \frac{2-1}{2} = \frac{2}{2}- \frac{1}{2}  \\  \frac{1}{2*3}= \frac{3-2}{3*2}= \frac{3}{3*2}- \frac{2}{3*2}= \frac{1}{2}- \frac{1}{3}
Adica scriem numaratorul fiecarei fractii ca diferenta dintre factorii de la numitor, si apoi scriem aceea fractie ca o diferenta de doua fractii si le simplificam. 
Obtinem: 1+ \frac{1}{2}- \frac{1}{2} + \frac{1}{3} - \frac{1}{3}+...- \frac{1}{49} + \frac{1}{49} - \frac{1}{50}
 Apoi reducem termenii asemenea. de ex  +\frac{1}{2} cu - \frac{1}{2}   si o sa obtinem  1- \frac{1}{50}= \frac{50}{50} - \frac{1}{50}= \frac{49}{50}


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