\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{200.201}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{200}-\frac{1}{201}\)

=\(\frac{1}{2}-\frac{1}{201}\)

=\(\frac{199}{402}\)

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{200.201}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{200}-\frac{1}{201}\)

\(=\frac{1}{2}-\frac{1}{201}=\frac{199}{402}\)

a=1.2+2.3+3.4+4.+....+200.201

3A = 1.2.(3 - 0) + 2.3.(4 - 1) + .... + 200.201.(202 - 199)

3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + .... + 200.201.202

3A = 200.201 . 202

A = 2706800

\(A=1.2+2.3+3.4+...+200.201\)

\(\frac{1}{A}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{200.201}\)

\(\frac{1}{A}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{200}-\frac{1}{201}\)

\(\frac{1}{A}=\frac{1}{1}-\frac{1}{201}=\frac{200}{201}\)

\(A=1:\frac{200}{201}=\frac{1.201}{200}=\frac{201}{200}\)

( Số cuối + Số đầu ) . số số hạng : 2 =a

A=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9

A=1/3-1/9

A=2/9

các câu 2;3 còn lại giống câu 1 bạn nhé

bạn thay số vào rồi làm tương tự

A=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9

A=1/3-1/9

A=2/9.

A= 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6

A= 1/2 - 1/3+ 1/3-1/4 + 1/4-1/5+ 1/5-1/6

A= 1/2- 1/6

A= 1/3

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{6}\)

\(\Rightarrow A=\frac{1}{3}\)

Wa cảm ơn các bạn nhiều nha

\(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{200.201}\)

=\(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{200}-\dfrac{1}{201}\)

=\(\dfrac{1}{3}-\dfrac{1}{201}\)

=\(\dfrac{67}{201}-\dfrac{1}{201}\)

=\(\dfrac{66}{201}\)

                         ---Học Tốt Nha---

Giải:

1/3.4+1/4.5+1/5.6+...+1/200.201

=1/3-1/4+1/4-1/5+1/5-1/6+...+1/200-1/201

=1/3-1/201

=22/67

Chúc bạn học tốt!

A = 2 + 3.4 + 5.6 + 7.7 + 8.8 + 9...199 + 200.201 + 202

A = SCSH: ( 202 - 2 ) : 2 + 1 = 101 ( số hạng )

A = Tổng: ( 202 + 2 ) . 101 : 2 = 10302

Vậy Tổng của A = 10302

Hk tốt,

k nhé

Cảm ơn nhé!

1/6 nhe

\(=\frac{1}{6}\)

\(\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}.\frac{3^2}{3\cdot4}\cdot\frac{4^2}{4\cdot5}\cdot\frac{5^2}{5\cdot6}\)

\(=\frac{1\cdot1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot5}{1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot6}\)

\(=\frac{1}{6}\)

gọi tổng là S ta có

3S=1.2.3-0.1.2+2.3.4-1.2.3+......+99.100.101-98.99.100

=>3S=98.99.100

=>S=\(\frac{98.99.100}{3}=323400\)

333300