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Aratati ca numarul a este natural,unde a=(2/1•3+2/3•5+2/5•7+...+2/27•29)•29/14

Răspuns :

Am atasat rezolvarea!
Vezi imaginea LUCASELA
[tex] \frac{2}{1*3}=1- \frac{1}{3} [/tex]
[tex] \frac{2}{3*5}=\frac{1}{3}- \frac{1}{5} [/tex]
[tex] \frac{2}{5*7}=\frac{1}{5}- \frac{1}{7} [/tex]
.................
[tex] \frac{2}{27*29}=\frac{1}{27}- \frac{1}{29} [/tex]
Daca adunam obtinem:
[tex] (1-\frac{1}{29})*\frac{29}{14}=2[/tex]