Ta có: A = 1.2 + 2.3 + 3.4 + 4.5 +.....+ 98.99

=> 3A = 1.2.(3 - 0) + 2.3.(4 - 1) + ..... +98.99.(100 - 97)

=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 98.99.100

=> 3A = 98.99.100

=> A = 98.99.100 / 3

=> A = 323400

G= \(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1.2+2.3+3.4+...+98.99}\)

G= \(\frac{\frac{1.2}{2}+\frac{2.3}{2}+\frac{3.4}{2}+...+\frac{98.99}{2}}{1.2+2.3+3.4+...+98.99}\)

G = \(\frac{\frac{1.2+2.3+...+98.99}{2}}{1.2+2.3+3.4+...+98.99}\)

G= \(\frac{1}{2}\)

mh chịu thôi

mình chiụ thôi, bó tay luôn

Gọi tổng trên là A
A=1/1.2.3+1/2.3.4+1/3.4.5+...1/98.99.100
Ta xét :
1/1.2 ‐ 1/2.3 = 2/1.2.3; 1/2.3 ‐ 1/3.4 = 2/2.3.4;...; 1/98.99 ‐ 1/99.100 = 2/98.99.100
tổng quát: 1/n﴾n+1﴿ ‐ 1/﴾n+1﴿﴾n+2﴿ = 2/n﴾n+1﴿﴾n+2﴿.
Do đó: 2A = 2/1.2.3 + 2/2.3.4 + 2/3.4.5 +...+ 2/98.99.100
= ﴾1/1.2 ‐ 1/2.3﴿ + ﴾1/2.3 ‐ 1/3.4﴿ +...+ ﴾1/98.99 ‐ 1/99.100﴿
= 1/1.2 ‐ 1/2.3 + 1/2.3 ‐ 1/3.4 + ... + 1/98.99 ‐ 1/99.100
= 1/1.2 ‐ 1/99.100
= 1/2 ‐ 1/9900
= 4950/9900 ‐ 1/9900
= 4949/9900.
Vậy A = 4949 / 9900

Bn làm sai r . kết quả là \(\frac{101}{297}\) nhưng mik ko bt cách giải thôi

xin lỗi nha,gửi lời giải nhầm người

\(A-1=\frac{1}{1.2}+\frac{1}{2.3}..+\frac{1}{99.100}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+..+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}\)\(=\frac{99}{100}\)

\(A=1+\frac{99}{100}=\frac{199}{100}\)

=1+1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100
=1+1/2+1/2-1/100

=199/100

A=1+1/2+1/2.3+1/3.4+...+1/98.99+1/99.100

A=1+1/1-1/2+1/2-1/3+1/4+...+1/98-1/99+1/99-1/100

A-1=1-1/100

A-1=99/100

A=99/100+1

A=199/100

Vậy A=199/100 

\(1+\frac{1}{2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(=1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(=2-\frac{1}{100}\)

\(=\frac{199}{100}\)

Gọi biểu thức là A

A=1+1/2+1/2.3+1/3.4+...+1/98.99+1/99.100

A-1=1/2+1/2.3+1/3.4+...+1/98.99+1/99.100

A-1=1-1/2+1/2-1/3+1/3-1/4+...+/198-1/99+1/99-1/100

A-1=1-1/100

A-1=99/100

A=99/100+1

A=199/100

cái này bấm máy tính cũng ra nek

a-b=(1.2+2.3+3.4+4.5+...+98.99)-(1²+2²+3²+...+98²)

1.2+2.3+3.4+4.5+...+98.99-1²-2²-3²-...-98²

^{=1(2-1)+2(3-2)+...+98(99-98)}

^=1+2+...+98

Đến đây bạn tự tính

b=1²+2²+3²+............+98²

b=1.(2-1)+2.(3-1)+3.(4-1)+..............+98.(99-1)

b=1.2-1+2.3-2+3.4-3+.............+98.99-98

b=(1.2+2.3+3.4+..................+98.99)-(1+2+3+............+98)

a-b=1+2+3+...............+98

a-b=\(\frac{98.\left(98+1\right)}{2}\)

a-b=4851

                                   Vậy A-B=4851