tính giá trị của đa thức A (x) = x+x^2+x^3+…+x^91+x^100 tại x= 1/2 13/08/2021 Bởi Amaya tính giá trị của đa thức A (x) = x+x^2+x^3+…+x^91+x^100 tại x= 1/2
Cho `x= 1/2` `=> A(1/2) = 1/2 + 1/2^2 + 1/2^3+…+1/2^99+ 1/2^100` `=> 1/2 A(1/2)= 1/2 ( 1/2 + 1/2^2 + 1/2^3 +…+1/2^99 + 1/2^100)` `=> 1/2 A(1/2) = 1/2^2 + 1/2^3 +….+1/2^100 + 1/2^101` `=> A(1/2) – 1/2A (1/2)= 1/2 + 1/2^2 + 1/2^3 +…+1/2^100 – 1/2^2 – 1/2^3 -….-1/2^100 – 1/2^101` `=> 1/2 A(1/2)= 1/2 – 1/2^101` `=> A(1/2) = (1/2 – 1/2^101): 1/2` `=> A(1/2) = (1/2 – 1/2^101) . 2` `=> A(1/2) = 1 – 1/2^100` Vậy `A(1/2) = 1- 1/2^100` Bình luận
Thay x=1/2 vào đa thức A , ta được : A(1/2)=1/2+1/2²+….+1/$2^{100}$ ⇒1/2 A (1/2) = 1/2+1/2²+….+1/$2^{101}$ ⇒(1-1/2).A(1/2)=1/2-1/$2^{100}$ ⇒A(1/2)=(1/2-1/$2^{100}$):1/2 ⇒A(1/2)=1-1/$2^{100}$ Bình luận
Cho `x= 1/2`
`=> A(1/2) = 1/2 + 1/2^2 + 1/2^3+…+1/2^99+ 1/2^100`
`=> 1/2 A(1/2)= 1/2 ( 1/2 + 1/2^2 + 1/2^3 +…+1/2^99 + 1/2^100)`
`=> 1/2 A(1/2) = 1/2^2 + 1/2^3 +….+1/2^100 + 1/2^101`
`=> A(1/2) – 1/2A (1/2)= 1/2 + 1/2^2 + 1/2^3 +…+1/2^100 – 1/2^2 – 1/2^3 -….-1/2^100 – 1/2^101`
`=> 1/2 A(1/2)= 1/2 – 1/2^101`
`=> A(1/2) = (1/2 – 1/2^101): 1/2`
`=> A(1/2) = (1/2 – 1/2^101) . 2`
`=> A(1/2) = 1 – 1/2^100`
Vậy `A(1/2) = 1- 1/2^100`
Thay x=1/2 vào đa thức A , ta được :
A(1/2)=1/2+1/2²+….+1/$2^{100}$
⇒1/2 A (1/2) = 1/2+1/2²+….+1/$2^{101}$
⇒(1-1/2).A(1/2)=1/2-1/$2^{100}$
⇒A(1/2)=(1/2-1/$2^{100}$):1/2
⇒A(1/2)=1-1/$2^{100}$