Question

[HaNa thân yêu]

a.1152 - (374+1152)+(-65+374)

b.13-12+11+10-9+8-7-6+5-4+3+2-1

c. tinh tong S = 1.2 + 2.3 + 3.4 + ..... + 99.100

d. chung minh rang : 1/2²+1/3² +1/4² + ..... + 1/100² < 1

Answer 1

[Đinh Đức Hùng]

c ) S = 1.2 + 2.3 + 3.4 + .... + 99.100

=> 3S = 1.2.3 + 2.3.3 + 3.4.3 + .... + 99.100.3

=> 3S = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + .... + 99.100.( 101 - 98 )

=> 3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + .... + 99.100.101 - 98.99.100

=> 3S = ( 1.2.3 - 1.2.3 ) + ( 2.3.4 - 2.3.4 ) + .... + ( 98.99.100 - 98.99.100 ) + 99.100.101

=> 3S = 99.100.101 => S = \(\frac{99.100.101}{3}\)

d ) Ta có \(\frac{1}{2^2}<\frac{1}{2.1}=\frac{1}{1}-\frac{1}{2}\)

               \(\frac{1}{3^2}<\frac{1}{2.3}=\frac{1}{2}-\frac{1}{3}\)

                ..........

                \(\frac{1}{100^2}<\frac{1}{99.100}=\frac{1}{99}-\frac{1}{100}\)

Vậy \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{100^2}<\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\)

 \(\Leftrightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{100^2}<\frac{1}{1}-\frac{1}{100}=\frac{99}{100}<1\)

Answer 2

[cao nguyễn thu uyên]

a,b đề là j bn???????????