Question

Calculati :

a) S= 2/1*3 + 2/3*5+2/5*7+...+2/97*99;

b)S=3/1*4+3/4*7+3/7*10+...+2/94*97

Answer 1

a)  S =1/1 -1/3 + 1/3 - 1/5 + 1/5 - 1/7 +......+1/97 - 1/99 = 1 - 1/99 = 98/99
b)  S = 1/1 - 1/4 + 1/4 - 1/7 +.......+1/94 - 1/97 = 1 - 1/97 = 96/97

Answer 2

punctul a) ... vezi atasamentul 1 !
pinctul b) ... sa foloseaste formula :  $\frac{3}{k(k+3}=\frac{1}{k}-\frac{1}{k+3} \;\;!$