Đặt S = 1 x 2 + 2 x 3 + ..... + 9 x 10

3S = 1 x 2 x (3-0) + 2 x 3 x (4 - 1) + ....... + 9 x 10 x (11 - 8)

3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ......... + 9 x 10 x 11 - 8 x 9 x 10

3S = ( 1 x 2 x 3 -1 x 2 x 3) + ( 2 x 3 x4 - 2 x 3 x 4) + ..... + (8 x 9  x 10 - 8 x 9 x 10) + 9 x 10 x 11

3S = 9 x 10 x 11 = 990

S = 990 : 3 = 330     

A=1/1*2+1/2*3+...+1/9*10

=1-1/2+1/2-1/3+...+1/9-1/10

=(1-1/10)+(1/2-1/2)+...+(1/9-1/9)

=(10/10-1/10)+0+...+0=9/10

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}=1-\frac{1}{10}=\frac{9}{10}\)

5

10

15

20

25

30

35

40

45

1+1+1+1+1=...?

2+2+2+2+2=...?

3+3+3+3+3=...?

4+4+4+4+4=4x5=20

5+5+5+5+5=5x5=25

6+6+6+6+6=6x5=30

7+7+7+7+7=7x5=35

8+8+8+8+8=8x5=40

9+9+9+9+9=9x5=45

1+1+1+1+1=5

2+2+2+2+2=10

3+3+3+3+3=15

4+4+4+4+4=20

5+5+5+5+5=25

6+6+6+6+6=30

7+7+7+7+7=35

8+8+8+8+8=40

9+9+9+9+9=45

1/10x(2/9x9/2)x(3/8x8/3)x(5/6x6/5)=1/10x1x1x1=1/10

a)2+4+8+6+7+8+3+9+2+1;

=(9+1)+(2+8)+(4+6)+(7+3)+(2+8)

=10+10+10+10+10

=10x5

=50

b)3+2+4+9+7+1+8+6+3+5

làm tương tự nhé

c)2+3+4+5+6+7+8+9+1+4.

làm tương tự nhé

P/s tham khảo nha

a) Bạn gộp các số có tổng bằng 10 :2-8,4-6,7-3,8-2,9-1 kq50

b)c) tương tự 

\

a)2+4+8+6+7+8+3+9+2+1

=(2+8)+(4+6)+(7+3)+(8+2)+(9+1)

=10+10+10+10+10

=50

b)3+2+4+9+7+1+8+6+3+5

=(3+7)+(2+8)+(4+6)+(9+1)+(3+5)

=10+10+10+10+8

=48

c)2+3+4+5+6+7+8+9+1+4

=(2+8)+(3+7)+(4+6)+(9+1)+(5+4)

=10+10+10+10+9

=49

tổng quát: \(\frac{1}{n.\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

Ta có: \(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{3}-\frac{1}{10}=\frac{10}{30}-\frac{3}{30}=\frac{7}{30}\)