đặt A=1/3²+1/4²+1/5²+……1/100²
B=1/2.3+1/3.4+...+1/99.100
=1/2-1/3...+1/99-1/100
=1/2-1/100<1/2 (1)
mà A=1/3²+1/4²+1/5²+……1/100²<B=1/2.3+1/3.4+...+1/99.100 (2)
kết hợp từ (1),(2)ta được A<B<1/2
=>A<1/2
Chung minh1/3^2+1/4^2+1/5^2+..........+1/100^2<1/2
Lam on giai ki giup minh. Minh can trong 30 phut nua
chung minh1/2^2+1/4^2+1/6^2+...........+1/2016^2<1/2
chung minh rang 1/3^2+1/4^2+1/5^2+...+1/100^2<1/2
chung minh rang :
1/3^2+1/4^2+1/5^2+1/6^2+...+1/100^2<1/2
1.Chưng minh rằng (1+/1/3+1/5+....+1/99)-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
2.Áp dụng phan 1 để chung minh 1-1/2+1/3-1/4+.....-1/200=1/101+1/102+.......+1/200
cho A =1/2*3/4*5/6*...*99/100
B=2/3*4/5*6/7*...*100/101
C=1/2*2/3*4/5*...*98/99
a) so sanh A, B, C
b) Chung minh: A*C< A^2< 1/10
c) Chung minh: 1/15< A< 1/10
Lam giup minh di ai lam duoc minh tich dung cho
chứng minh
1/4+1/16+1/36+...+196 < 1/2
cho đáp án với <333
chung minh rang : 1 / 2 ^ 2 + 1 / 3 ^ 2 + 1 / 4 ^ 2 + . . . + 1 / 100 ^ 2 < 99 / 100
bai 5 : tinh
a) tim x , biet (x+1) +(x+2 ) + ...+(x+100)=5750
b) chung minh rang B = 1/2^2 + 1/3^2 + 1/4^2 + ...+1/2021^2 < 1
giup mik luon voi
