Question

AJUTORRRRRRRRRRRRRRRRRRRRRRRRRRRRRR!! Calculați ​

Answer 1

$\frac{3}{5} +\frac{3}{45} +\frac{3}{117} +...+\frac{3}{1517} +\frac{3}{1846} +\frac{3}{2205} =$

descompunem numitorul in produs de 2 factori

$\frac{3}{1X5} +\frac{3}{5X9} +\frac{3}{9X13} +...+\frac{3}{37X41} +\frac{3}{41X45} +\frac{3}{45X49} =$

dupa care se foloseste formula speciala, cred ca o stii... ca nu mai am rabdare sa scriu :)))

rezultatul semifinal fiind:

1-1/49

se amplifica primul 1 cu 49 pentru efectuarea scaderii, iar rexultatul final va fi...

$\frac{48} {49}$

DACA NU STII FORMULA SPUNE IN COMENTARII CA TI O ZIC

Answer 2

Răspuns:

Explicație pas cu pas:

$\frac{3}{5} +\frac{3}{45} +\frac{3}{117} +\frac{3}{221} +...+\frac{3}{1845}+\frac{3}{2205} =\\ \\ 3(\frac{1}{5} +\frac{1}{45} +\frac{1}{117} +\frac{1}{221} +...+\frac{1}{1845}+\frac{1}{2205} )=\\ \\ 3(\frac{1}{1} \frac{1}{5} +\frac{1}{5} \frac{1}{9} +\frac{1}{9} \frac{1}{13} +\frac{1}{13} \frac{1}{17} +...+\frac{1}{41} \frac{1}{45} +\frac{1}{45} \frac{1}{49} )=$

$3(\frac{1}{1}- \frac{4}{5} +\frac{4}{5} -\frac{7}{9} +\frac{7}{9} -\frac{10}{13} +\frac{10}{13}- \frac{13}{17} +\frac{31}{41}- \frac{34}{45} +\frac{34}{45} -\frac{37}{49} )=\\ \\ 3(1-\frac{37}{49} )=3x \frac{49-37}{49} =3x\frac{12}{49} =\frac{36}{49}$