Question

Va rog noua și zece dau coroana mulțumesc si puncte

Answer 1

Răspuns:

9.a)

$\frac{1}{30*31}+\frac{1}{31*32}+\frac{1}{32*33}+...+\frac{1}{89*90}=\frac{31-30}{30*31}+\frac{32-31}{31*32}+\frac{33-32}{32*33}+...+\frac{90-89}{89*90}=\frac{31}{30*31}-\frac{30}{30*31}+\frac{32}{31*32}-\frac{31}{31*32}+\frac{33}{32*33}-\frac{32}{32*33}+...+\frac{90}{89*90}-\frac{89}{89*90}=\frac{1}{30}-\frac{1}{31}+\frac{1}{31}-\frac{1}{32}+\frac{1}{32}-\frac{1}{33}+...+\frac{1}{89}-\frac{1}{90}=\frac{1}{30}-\frac{1}{90}=\frac{3-1}{90}=\frac{2}{90}=\frac{1}{45}$

b)

$\frac{3}{5*8}+\frac{3}{8*11}+\frac{3}{11*14}+...+\frac{3}{47*50}=\frac{8-5}{5*8}+\frac{11-8}{8*11}+\frac{14-11}{11*14}+...+\frac{50-47}{47*50}=\frac{8}{5*8}-\frac{5}{5*8}+\frac{11}{11*8}-\frac{8}{11*8}+\frac{14}{11*14}-\frac{11}{14*11}+...+\frac{50}{50*47}-\frac{47}{47*50}=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{11}{47}-\frac{1}{50}=\frac[1}{5}-\frac{1}{50}=\frac{10-1}{50}=\frac{9}{50}$

10. $\frac{15}{2x+1}$∈N ⇔2x+1∈D15

D15={1,3,5,15}

2x+1=1   2x=0  x=0

2x+1=3   2x=2  x=1

2x+1=5    2x=4   x=2

2x+1=15   2x=14  x=7

Explicație pas cu pas: