Question

Se considera a=2/1x3 +2/3x5 + ... + 2/49x51. Stabiliti daca a∈(1/2 ;1)

Answer 1

a=2/(1x3) +2/(3x5) + ... + 2/(49x51)

a=(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+......+(1/49-1/51)

a=1/1-1/51

a=50/51

1/2=50/100 si 1=50/50

=> 50/100<50/51<50/50

sau 1/2<50/51<1 ; 1/2<a<1

=> a∈(1/2; 1)