Toán tính: 1 + 3 + 3^2 + 3^3 + … + 3^100= ? jup mik vs 08/10/2021 By Autumn tính: 1 + 3 + 3^2 + 3^3 + … + 3^100= ? jup mik vs
B=1+3+3^2+…+3^100 3B=3+3^2+3^6+…+3^101 3B-B=(3+3^2+3^3+…+3^101)-(1+3+3^2÷…+3^100) 2B=3^101-1 B=3^101-1 2 Trả lời
Đặt $A = 1+3+3^2+….+3^{100}$ $\to 3A = 3+3^2+3^3+….+3^{101}$ $\to 3A-A = (3+3^2+3^3+….+3^{101})-(1+3+3^2+….+3^{100})$ $ \to 2A = 3^{101}-1$ $\to A = \dfrac{3^{101}-1}{2}$ Trả lời
B=1+3+3^2+…+3^100
3B=3+3^2+3^6+…+3^101
3B-B=(3+3^2+3^3+…+3^101)-(1+3+3^2÷…+3^100)
2B=3^101-1
B=3^101-1
2
Đặt $A = 1+3+3^2+….+3^{100}$
$\to 3A = 3+3^2+3^3+….+3^{101}$
$\to 3A-A = (3+3^2+3^3+….+3^{101})-(1+3+3^2+….+3^{100})$
$ \to 2A = 3^{101}-1$
$\to A = \dfrac{3^{101}-1}{2}$