Đáp án:
Giải thích các bước giải:
`C=1/5+1/5^2+1/5^3+...+1/5^100`
`=>5C=1+1/5+1/5^2+...+1/5^99`
`=>5C-C=(1+1/5+1/5^2+...+1/5^99)-(1/5+1/5^2+1/5^3+...+1/5^100)`
`=>4C=1-1/5^100`
`=>`$C=\dfrac{1-\dfrac{1}{5^{100}}}{4}$
`D=2/3+8/3^2+26/3^3+...+(3^100-1)/3^100`
`=>D=(1-1/3)+(1-1/3^2)+(1-1/3^3)+...+(1-1/3^100)`
`=>D=100-(1/3+1/3^2+1/3^3+...+1/3^100)`
`=>D'=1/3+1/3^2+1/3^3+...+1/3^100`
`=>3D'=1+1/3+1/3^2+...+1/3^99`
`=>2D'=1-1/3^100`
`=>D=100-(1-1/3^100)`
`=>D=99+1/3^100`
`F=3/(1^2. 2^2)+5/(2^2. 3^2)+...+4033/(2016^2. 2017^2)`
`=>F=1-1/2^2+1/2^2-1/3^2+...+1/2016^2-1/2017^2`
`=>F=1-1/2017^2`
`=>F=(2017^2-1)/2017^2`
`G=((-4)/7)+((-4)/7)^2+((-4)/7)^3+...+((-4)/7)^2021`
`=>(-4G)/7=((-4)/7)^2+((-4)/7)^3+((-4)/7)^4+...+((-4)/7)^2022`
`=>(-5G)/7=((-4)/7)^2022+4/7`
`=>G=((-4)/7)^2022+4/7)/((-5)/7)`
