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Adrian
Vizitator
2016-05-19 08:49:20

Buna ziua


sa se calculeze:



multumesc

G.K.
Vizitator
2016-05-19 20:39:36

9k2 + 3k - 2 = (3k-1)(3k+2).


(6k+1)/(9k2+3k-2)2 = (6k+1)/[(3k-1)(3k+2)]2


= (3k-1)/[(3k-1)(3k+2)]2 + (3k+2)/[(3k-1)(3k+2)]2 = 1/[(3k-1)(3k+2)2] + 1/[(3k-1)2(3k+2)] = 


= 1/[(3k-1)(3k+2)]*[1/(3k-1) + 1/(3k+2)] = (1/3)*[1/(3k-1) - 1/(3k+2)]*[1/(3k-1) + 1/(3k+2)] =


= (1/3)*[1/(3k-1)2 - 1/(3k+2)2].  


Suma de calculat este o suma telescopica, 


S = (1/3)*[1/22 - 1/52 + 1/52 - 1/82 + ... + 1/1972 - 1/2002] = (1/3)*[1/22 - 1/2002] = (1/3)*(9999/40000) = 3333/40000,  varianta corecta de raspuns este b). 

Adrian
Vizitator
2016-05-19 22:16:44

am inteles multumescSmile

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