bn giở sách phát triển nâng cao ra là có mà

ta đặt vế trái là A ta có:

A=1/2.2 .(1+1/2.2+1/3.3+1/4.4+...+1/50.50)

A< 1/2.2.(1+1/1.2+1/2.3+1/3.4+1/4.5+...+1/49.50)

A< 1/2.2.(1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+....+1/49-1/50)

A< 1/2.2.(1+1-150)

A< 1/2.2.99/50

A< 1/4.99/50

A< 99/200<100/200=1/2

=>A<1/2

1 + 2 x 2 + 3 x 3 + 4 x 4 + 5 x 5 + 6 x 6 + 7 x 7 + 8 x 8 + 9 x 9 + 10 x 10

= 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100

= 385

1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7 + 8x8 + 9x9 + 10x10

= 1+4+9+16+25+36+49+64+81+100

=(81+9)+(64+16)+(49+1)+)36+4)+25+100

=90+80+50+40+25 +100

=385

Đặt T = 1 + 2 x 2 + ... + 10 x 2 = 385

1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81 
10 x 10 = 100
 

\(1x1=1\)

\(2x2=4\)

\(3x3=9\)

\(4x4=16\)

\(5x5=25\)

\(6x6=36\)

\(7x7=49\)

\(8x8=64\)

\(9x9=81\)

\(10x10=100\)

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 = 49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100

đặt \(A=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+\frac{1}{5.5}+\frac{1}{6.6}+\frac{1}{7.7}+\frac{1}{8.8}=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)

\(A

a)=1x2x3x4x5/2x3x4x5x6 =1/6

b)=1x2x3x4x5x6x7x8x9/10x9x8x7x6x5x4x3 x2=1/10