Question

chờ A(x)=x+x^2+x^3+...+x^100.Tính A(1/2) giải chi tiết cho mình nha

Answer 1

Sửa lại:A.x=x²+x³+...+x¹⁰¹

=>A.x-A=(x²+x³+...+x¹⁰¹)-(x+x²+...+x¹⁰⁰)

=>A(x-1)=x¹⁰¹-x

=>A=\(\dfrac{x^{101}-x}{x-1}\)

Thay x=\(\dfrac{1}{2}\)vào A ta có:

A=\(\dfrac{\left(\dfrac{1}{2}\right)^{101}-\dfrac{1}{2}}{\dfrac{1}{2}-1}=\dfrac{\left(\dfrac{1}{2}\right)^{101}-\dfrac{1}{2}}{-\dfrac{1}{2}}=1-\left(\dfrac{1}{2}\right)^{100}=\dfrac{2^{100}-1}{2^{100}}\)

Answer 2

Ta có:A.x=x²+x³+...+x¹⁰¹

=>A.x-A=(x²+x³+...+x¹⁰¹)-(x+x²+...+x¹⁰⁰)

=>A(x-1)=x¹⁰¹-x

=>A=\(\dfrac{x^{101}-x}{x-1}\)

Thay x=\(\dfrac{1}{2}\)

=>A=\(\dfrac{\left(\dfrac{1}{2}\right)^{101}-\dfrac{1}{2}}{\dfrac{1}{2}-1}=\dfrac{\left(\dfrac{1}{2}\right)^{101}-\dfrac{1}{2}}{-\dfrac{1}{2}}=1-\left(\dfrac{1}{2}\right)^{101}\)