A=\(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}\)

⇒3A=\(1+\dfrac{2}{3}+\dfrac{3}{3^2}+...+\dfrac{100}{3^{99}}\)

⇒\(3A-A=\left(1+\dfrac{2}{3}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{99}}\right)-\left(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}\right)\)

⇒\(2A=1+\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)-\dfrac{100}{3^{100}}\)

⇒\(2A=1+\dfrac{1}{2}-\dfrac{1}{2\cdot3^{99}}-\dfrac{100}{3^{100}}\)

⇒\(A=\dfrac{3}{4}-\dfrac{1}{4\cdot3^{99}}-\dfrac{50}{3^{100}}< \dfrac{3}{4}\)

Vậy......

đk xđ : x - 5 > 0 ⇔ x > 5

Diện tích viên gạch:

`60xx60=3600(cm^2)`

Diện tích căn phòng là:

`3600xx400=1440000(cm^2)=144(m^2)`

D/s....

giúp tui trl ddii ><

`1/[5.6]-1/[6.7]-1/[7.8]-...-1/[3.2]-1/[2.1]`

`=1/5-1/6-1/6+1/7-1/7+1/8-...-1/3+1/2-1/2+1`

`=1/5-1/3+1`

`=13/15`

Sửa: `4/[3.7]+4/[7.11]+...+4/[95.99]`

`=1/3-1/7+1/7-1/11+....+1/95-1/99`

`=1/3-1/99`

`=32/99`

A = \(\dfrac{4}{3.7}\) + \(\dfrac{4}{7.11}\) + ......+ \(\dfrac{4}{95.99}\)

A = \(\dfrac{1}{3}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{11}\) + ......+ \(\dfrac{1}{95}\) - \(\dfrac{1}{99}\)

A = \(\dfrac{1}{3}\) - \(\dfrac{1}{99}\)

A = \(\dfrac{32}{99}\)