Question

Cho P = 1+1/2+1/3+1/4+...+1/2^100-1.CMR P > 50

Answer 1

P=1+1/2+1/3+1/4+...+1/2^100-1

suy ra P=1+1/2+1/3+1/2^2+...+1/2^100+1/2^100-1+1/2^100-1/2^100

suy ra P=1+1/2+(1/3+1/2^2)+(1/5+1/2^3)+...+(1/2^99+1+...+1/2^100)-1/2^100

suy ra P>1+1/2+1/2^2.2+1/2^3.3^2+...+1/2^100.2^99-1/2^100

suy ra P>1+1/2.100-1/2^100

suy ra P>51-1/2^100>51-1

suy ra P>50(đpcm)

Answer 2

P=1+1/2+1/3+1/4+...+1/2^100-1

suy ra P=1+1/2+1/3+1/2^2+...+1/2^100+1/2^100-1+1/2^100-1/2^100

suy ra P=1+1/2+(1/3+1/2^2)+(1/5+1/2^3)+...+(1/2^99+1+...+1/2^100)-1/2^100

suy ra P>1+1/2+1/2^2.2+1/2^3.3^2+...+1/2^100.2^99-1/2^100

suy ra P>1+1/2.100-1/2^100

suy ra P>51-1/2^100>51-1

suy ra P>50(đpcm)