Toán Lớp 6: cho S = 1/2 +1/3 +1/4+-+1/48+1/49+1/50 và P = 1/49+2/48+347+-+48/2+49/1 hãy tính S/P

Question

Toán Lớp 6:  cho S = 1/2 +1/3 +1/4+....+1/48+1/49+1/50 và P = 1/49+2/48+347+....+48/2+49/1 hãy tính S/P

thanhthuythu · Answer

Ta c&oacute;:       S = 1/2 + 1/3 + 1/4 + ... + 1/50        P = 1/49 + 2/48 + 3/47+ ... + 49/1       &rArr; S/P = 1/2 + 1/3 + 1/4 + ... + 1/50  /  1/49 + 2/48 + 3/47 + ... + 49/1        =1/2 + 1/3 + 1/4 +...+ 1/50  /  ( 1 + 1/49 ) + ( 1 + 2/48 ) + ... + ( 1 + 48/2 ) + 1          = 1/2 + 1/3 + 1/4 + ... + 1/50  /  50/49+50/48+50/47+...+50/2+50/50       1/2+1/3+1/4+...+1/50  /  50.( 1/2 + 1/3 + 1/4 + ... + 1/50 ) = 1/50       Vậy S/P = 1/50

behocgioitoan · Answer

$  $   P = 1/49 + 2/48 + ... + 48/2+ 49/1   -> P = 1/49 + 2/48 + ... + 48/2 + 49   -> P = 1/49 + 1/48 + ... + 48/2 +  underbrace{1+1+...+1}_{ text{49 số 1}}   -> P = (1/49 + 1)+(1/48+1)+...+(48/2+1)+1   -> P =(1/49 + 49/49)+(1/48 + 48/48)+...+(48/2 + 2/2)+50/50   -> P = 50/49 + 50/48 + ... + 50/2 + 50/50   -> P =50 (1/2 + 1/3+...+1/49 + 1/50)   $  $   S/P   = (1/2+1/3+...+1/49+1/50)/(50 (1/2 + 1/3+...+1/49+1/50) )   = ( cancel (1/2 +1/3+...+1/49+1/50) )/(50 ( cancel (1/2+1/3+...+1/49+1/50) )   = 1/50   $  $   Vậy S/P =1/50