Đặt A = 1 x 2 + 2 x 3 + 3 x 4 + ... + n x ( n - 1)
=> 3A = 1 x 2 x (3 - 0) + 2 x 3 x (4 - 1) + 3 x 4 x (5 - 2) + ... + n x (n - 1) x [(n + 2) x (n + 1)]
=> 3A = 1 x 2 x 3 - 1 x 2 x 3 + 2 x 3 x 4 - 2 x 3 x 4 + ... + n x (n + 1) x (n + 2)
=> 3A = n x (n + 1) x (n + 2)
=> A = n x (n + 1) x (n + 2) / 3

3S=1.2.3+3.4.5+...+n.(n-1).3

1.2.(3-0).......................................................

 k mk đi mk giải tiếp cho nha

Cám ơn bạn

cac cau tu di ma lam bai tap cua minh

cau len mang di , bai nay mk chua hoc , sory nha

chuc ban hoc tot ^-^

Đặt \(A=1\cdot2\cdot4+2\cdot3\cdot5+3\cdot4\cdot6+\cdots+100\cdot101\cdot103\)

\(=1\cdot2\cdot\left(3+1\right)+2\cdot3\cdot\left(4+1\right)+\cdots+100\cdot101\cdot\left(102+1\right)\)

\(=\left(1\cdot2\cdot3+2\cdot3\cdot4+\cdots+100\cdot101\cdot102\right)+\left(1\cdot2+2\cdot3+\cdots+100\cdot101\right)\)

Đặt \(B=1\cdot2\cdot3+2\cdot3\cdot4+\cdots+100\cdot101\cdot102\)

\(=\left(2-1\right)\cdot2\cdot\left(2+1\right)+\left(3-1\right)\cdot3\cdot\left(3+1\right)+\cdots+\left(101-1\right)\cdot101\cdot\left(101+1\right)\)

\(=2\left(2^2-1\right)+3\left(3^2-1\right)+\cdots+101\left(101^2-1\right)\)

\(=\left(2^3+3^3+\cdots+101^3\right)-\left(2+3+\cdots+101\right)\)

\(=\left(1^3+2^3+3^3+\cdots+101^3\right)-1-\left(2+3+\cdots+101\right)\)

\(=\left(1^3+2^3+\cdots+101^3\right)-\left(1+2+3+\cdots+101\right)\)

\(=\left(1+2+3+\cdots+101\right)^2-\left(1+2+3+\cdots+101\right)\)

\(=\left\lbrack101\cdot\frac{102}{2}\right\rbrack^2-101\cdot\frac{102}{2}=\left(101\cdot51\right)^2-101\cdot51\)

Đặt \(C=1\cdot2+2\cdot3+\cdots+100\cdot101\)

\(=1\left(1+1\right)+2\left(2+1\right)+\cdots+100\left(100+1\right)\)

\(=\left(1^2+2^2+\cdots+100^2\right)+\left(1+2+\cdots+100\right)\)

\(=\frac{100\left(100+1\right)\left(2\cdot100+1\right)}{6}+\frac{100\cdot101}{2}=\frac{100\cdot101\cdot201}{6}+50\cdot101\)

\(=50\cdot101\cdot67+50\cdot101=50\cdot101\cdot68\)

Ta có: A\(=\left(1\cdot2\cdot3+2\cdot3\cdot4+\cdots+100\cdot101\cdot102\right)+\left(1\cdot2+2\cdot3+\cdots+100\cdot101\right)\)

=B+C

\(=\left(101\cdot51\right)^2-101\cdot51+50\cdot101\cdot68\)

\(=101^2\cdot51^2-101\cdot51+50\cdot101\cdot68=101\left(101\cdot51^2-51+50\cdot68\right)=101\cdot266050\)

Đặt \(D=1\cdot2^2+2\cdot3^2+\cdots+100\cdot101^2\)

\(=2^2\left(2-1\right)+3^2\left(3-1\right)+\cdots+101^2\left(101-1\right)\)

\(=\left(2^3+3^3+\cdots+101^3\right)-\left(2^2+3^2+\cdots+101^2\right)\)

\(=\left(1^3+2^3+\cdots+101^3\right)-\left(1^2+2^2+\cdots+101^2\right)\)
\(=\left(1+2+\cdots+101\right)^2-101\cdot\frac{\left(101+1\right)\left(2\cdot101+1\right)}{6}\)

\(=\left(101\cdot\frac{102}{2}\right)^2-101\cdot17\cdot2023=101^2\cdot51^2-101\cdot17\cdot2023\)

\(=101\cdot17\left(101\cdot17\cdot3^2-2023\right)=101\cdot17\cdot13430\)

Ta có: \(\frac{1\cdot2\cdot4+2\cdot3\cdot5+3\cdot4\cdot6+\cdots+100\cdot101\cdot103}{1\cdot2^2+2\cdot3^2+\cdots+100\cdot101^2}\)

\(=\frac{101\cdot266050}{101\cdot17\cdot13430}=\frac{1565}{1343}\)

khó quá sai thì thôi nha

= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/49 - 1/50

= 1/1 - 1/50

= 49/50

1/1.2 + 1/2.3 + 1/3.4 +.....+ 1/49.50

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +......+ 1/49 - 1/50

= 1 - 1/50

= 49/50

1/1.2 + 1/2.3 + 1/3.4 +.....+ 1/49.50 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +......+ 1/49 - 1/50 = 1 - 1/50 = 49/50 

các bn chỉ cần làm bài 2 thôi nhé!mk biết làm bài 1 rùi.ai làm xong bài 2 trước ngày mai mk tích cho

làm ơn trả lời câu hỏi đi mà

=1999/1000

dung 10000000000000000000000000000000000000000% 

kết quả là 6015

\(A=1\times2+2\times3+3\times4+...+19\times20\)

\(A\times3=3\times\left(1\times2+2\times3+3\times4+...+19\times20\right)\)

\(A\times3=1\times2\times3+2\times3\times3+3\times4\times3+...+19\times20\times3\)

\(A\times3=1\times2\times3+2\times3\times\left(4-1\right)+3\times4\times\left(5-2\right)+....+19\times20\times\left(21-18\right)\)

\(A\times3=1\times2\times3-1\times2\times3+2\times3\times4-2\times3\times4+3\times4\times5+...+19\times20\times21\)

\(A\times3=\left(1\times2\times3-1\times2\times3\right)+\left(2\times3\times4-2\times3\times4\right)+...+\left(18\times19\times20-18\times19\times20\right)+19\times20\times21\)

\(A\times3=19\times20\times21\)

\(A\times3=7980\)

cảm ơn bạn nhiều nhé