Question

Pentru un ex.multumesc mult de ajutor!

Answer 1

$\frac{3}{1*4}+\frac{3}{4*7}+\frac{3}{7*10}+...+\frac{3}{25*28}$=$3*\frac{1}{3}*(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{25}-\frac{1}{28})$=$1-\frac{1}{28}=\frac{27}{28}$

$\frac{4}{1*5}+\frac{4}{5*9}+\frac{4}{9*13}+...\frac{4}{25*29}$=$4*\frac{1}{4}*(\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-...+\frac{1}{25}-\frac{1}{29})$=$1-\frac{1}{29}=\frac{28}{29}$

$\frac{27}{28}-\frac{28}{29}=\frac{27*29-28*28}{28*29}=-\frac{1}{812}$

Pentru aceste tipuri de exericitii, cand ai o suma de fractii cu un produs jos, numere consecutive se foloseste urmatoarea regula:

$\frac{1}{a*b}=\frac{1}{b-a}*(\frac{1}{a}-\frac{1}{b})$. In general se reduc toate inafara de primul si ultimul termen din suma.