=> 4E = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + .... + 99.100.101.4

=> 4E = 1.2.3.( 4 - 0 ) + 2.3.4.( 5 - 1 ) + 3.4.5.( 6 - 2 ) + .... + 99.100.101.( 102 - 98 )

=> 4E = 1.2.3.4 - 0.1.2.3 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 99.100.101.102 - 98.99.100.101

=> 4E = ( 1.2.3.4 - 1.2.3.4 ) + ( 2.3.4.5 - 2.3.4.5 ) +  + ... + ( 98.99.100.101 - 98.99.100.101 ) + 99.100.101.102

=> 4E = 99.100.101.102

=> E = ( 99.100.101.102 ) : 4

Ta có: A = 1.2.3+3.4.5+5.6.7+...+99.100.101

A = 1.3 (5-3) + 3.5 (7-3) + 5.7 (9-3) + ............ + 99.101 (103 - 3)

A = (1.3.5 + 3.5.7 + 5.7.9 + .......... + 99.101.103) - (1.3.3 + 3.5.3 + ....... + 99.101.3)

A = (15+99.101.103.105) : 8 - 3.(1.3 + 3.5 +5.7 + ...... + 99.101)

A = 13517400 - 3.171650

A = 13002450

1.2.3.4+2.3.4.5+3.4.5.6+...+97.98.99.100

4S=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100). 4

4S=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4S=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...98.99.100.101-97.98.99.100

4S=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98+99.100+101

4S=98.99.100.101

Vậy S = 98.99.100.101/4 = 24497550

\(A=1.2.3+3.4.5+5.6.7+...+99.100.+101\)

\(A=1.3\left(5-3\right)+3.5\left(7-3\right)+5.7\left(9-3\right)+...+99.100\left(103-3\right)\)

\(=\left(1.3.5+3.5.7+5.7.9+99.101.103\right)-\left(1.3.3+3.5.3+99.101.3\right)\)

\(=\left(15+99.101.103.105\right):8-3.\left(1.3+3.5+5.7+99.101\right)\)

\(=13517400-3.171650\)

\(=13002450\)

cau còn lại bạn trả lời được mình sẽ tích cho bạn luôn

Đúng ko 

Rút gọn mỗi số hãng của số ta được :

\(C=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

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

     \(=1-\frac{1}{101}=\frac{100}{101}\)

Vậy C = 100/101

\(C=\frac{4}{1.2.3}+\frac{8}{3.4.5}+\frac{12}{5.6.7}+...+\frac{200}{99.100.101}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

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

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

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

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

\(C=\frac{4}{1.2.3}+\frac{8}{3.4.5}+\frac{12}{5.6.7}+.....+\frac{200}{99.100.101}\)

\(C=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{99.101}\)

\(C=\frac{1}{2}\left(2-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+.....+\frac{2}{99}-\frac{2}{101}\right)\)

\(C=\frac{1}{2}\left(2-\frac{2}{101}\right)\)

\(C=\frac{1}{2}\left(\frac{202}{101}-\frac{2}{101}\right)\)

\(C=\frac{1}{2}.\frac{200}{101}\)

\(C=\frac{200}{202}=\frac{100}{101}\)

Đặt S= 1.2 + 2.3 + 3.4 + ...+ 99.100
 3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101  3S = 3.33.100.101 
 S=33.100.101= 333300

Đặt S = 1,2 + 2,3 + 3,4 + ... + 99.100

3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + 98.99.3 + 99.100.3

3S = 1.2.3 + 2.3 ( 4 - 1 ) + 3.4 ( 5 - 2 ) + ... + 98.99 ( 100 - 97 ) + 99.100 ( 101 - 98 )

3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... - 97.98.99 + 99.100.101 - 98.99.100

S = 33.100.101 = 333300

Vậy S bằng 333300

Đáp số : S : 333300

Đặt S=1.2.3+2.3.4+....+99.100.101

3S=1.2.3+2.3.3+3.4.3+....+98.99.3+100.101.3

3S=1.2.3+2.3(4-1)+3.4(5-2)+.....+98.99+99.100(101-98)

3S=1.2.3+2.3.4-1.2.3+3.4.5+3.4.5-2.3.4+......+97.98.99+99.100.101-98.99.100

3S=33.100.101=333300

Vậy S=333300

Đặt \(A=1.2.3+2.3.4+3.4.5+...+99.100.101\)

\(\Rightarrow4A=1.2.3.4+2.3.4.4+...+99.100.101.4\)

\(=1.2.3\left(4-0\right)+2.3.4\left(5-1\right)+...+99.100.101\left(102-98\right)\)

\(=\left(1.2.3.4+2.3.4.5+...+99.100+101.102\right)-\left(0.1.2.3+1.2.3.4+...+98.99.100.101\right)\)

\(=99.100.101.102-0.1.2.3\)

\(=101989800\)

\(\Rightarrow A=101989800:4=25497450\)

Vậy \(A=25497450.\)