Đặt biểu thức = A

6A = 1x3x6 + 3x5x6+....+ 97x99x6

= 1x3x(1+5) + 3x5x(7-1) + 5x7x(9-3) +.....+ 97x99x(101-95)

= 1x3+1x3x5+3x5x7-1x3x5+5x7x9-3x5x7+.....+97x99x101-95x97x99

= 1x3+97x99x101

= 969906

=> A = 161651

k mk nha

A=1x3 +3x5 +5x7 +....+99x101

6A=1x3x(5+1) + 3x5x(7-1) +5x7x(9-3) +...+ 99x101x(103-97)

6A=3+ 1x3x5 +3x5x7-1x3x5 + 5x7x9 -3x5x7 +....+99x101x103 - 97x99x101

6A=3+99x101x103=1019703

A=1x3+3x5+5x7+...+99x101

Ax6=1x3x6+3x5x6+5x7x6+....+99x101x6

Ax6=1x3x(5+1)+3x5x(7-1)+5x7x(9-3)+...+99x101x(103-97)

Ax6=1x3x5+1x1x3+3x5x7-1x3x5+5x7x9-3x5x7+..+99x101x103-97x99x101

Ax6=1x3x1+99x101x103

Ax6=3+1029897

Ax6=1029900

A=1029900:6

A=171650

(Đặt A là tên biểu thức)

chịu

A=1x3x(5+1) + 3x5x(7-1) +5x7x(9-3) +...+ 99x101x(103-97)

6A=3+ 1x3x5 +3x5x7-1x3x5 + 5x7x9 -3x5x7 +....+99x101x103 - 97x99x101

6A=3+99x101x103=1019703

vậy = 1019703

nếu sai chỗ nào thì sửa hộ mk vs

\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{99\cdot101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

2/1.3 + 2/3.5 + 2/5.7 + ... + 2/99.101

= 2 .( 1/1.3 + 1/3.5 + 1/5.7 + ... + 1/99.101 ) 

= 2 . ( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/99 - 1/101 ) 

= 2 . ( 1 - 1/101 ) 

= 2 . ( 101/101 - 1/101 ) 

= 2 . 100/101

= 200/101

Chúc bn hok tốt !!!

Câu a:

A = 1.2 + 2.3 + 3.4 + ...+ 99.100

3A = 1.2.3 + 2.3.3 +..+ 99.100.3

1.2.3 = 1.2.3

2.3.3 = 2.3(4 - 1) = 2.3.4 - 1.2.3

3.4.4 = 3.4(5 - 2) = 3.4.5 - 2.3.4

.............................................................

99.100.3 = 99.100.(101 - 98)=99.100.101-98.99.100

Cộng vế với vế ta có:

3A = 99.100.101

A = 99.100.101 : 3

A = 333300

Câu b:

1.3 + 3.5 + 5.7 + ..+ 97.99

6.A = 1.3.6 + 3.5.6 + 5.7.6 + ...+ 97.99.6

1.3.6 = 1.3.(5 + 1) = 1.3.5 + 1.3.1

3.5.6 = 3.5.(7 - 1) = 3.5.7 - 1.3.5

5.7.6 = 5.7.(9 - 3) = 5.7.9 - 3.5.7

.......................................................

97.99.6 = 97.99.(101 - 95) = 97.99.101-95.97.99

Cộng vế với vế ta có:

6A = 1.3.1 + 97.99.101

A = (1.3.1 + 97.99.101) : 6

A = (3 + 9603.101) : 6

A = (3+ 969903) : 6

A = 969906 : 6

A = 161651