gọi 1+2^2+2^3+....+2^100 là A
TA co :
2A=2.(2^0+2^1+....+2^100)
2A= 2^1+2^2+2^3+....+2^101
2A-A=A suy ra A= 2^101-1
SUY RA 1+2^2+.......+2^100=2^101-1
chung to rang 1/2^2+1/3^2+1/4^2+....+1/100^2 <1
cho c =1+4+4^2+...+4^100 va b =4^101 . chung minh rang c<b/3
chung to raNG
1-1/2+1/3-1/4+.......................+1/199_1/200=1/101+1/102+............+1/2000
chung to rang 1/101+1/102+...+1/299+1/300>2/3
Chung to rang:1+1/2 mu2+1/3 mu2+1/4 mu2+....+1/100 mu2 be hon 2
cho P=1+1/2+1/3+1/4+...+1/2^100-1. chung to rang P<50
chung minh rang : 1 / 2 ^ 2 + 1 / 3 ^ 2 + 1 / 4 ^ 2 + . . . + 1 / 100 ^ 2 < 99 / 100
chung minh rang 1/3^2+1/4^2+1/5^2+...+1/100^2<1/2
chung minh rang 1-1/2^2-1/3^3-1/4^2-....-1/100^2>1/100
please,who can help me?
