Question

[tran thu thuy]

tính tổng

a) D=1/7+1/7²+1/7³+...+1/7¹⁰⁰

E=4/5+4/5²-4/5³+...+4/5²⁰⁰

giúp mình nhé mình đang cần ai giải nhanh nhất mình tick cho

Answer 1

[Nguyễn Huy Tú]

a) \(D=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\)

\(\Rightarrow7D=1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{99}}\)

\(\Rightarrow7D-D=\left(1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{99}}\right)-\left(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\right)\)

\(\Rightarrow6D=1-\frac{1}{7^{100}}\)

\(\Rightarrow D=\left(1-\frac{1}{7^{100}}\right).\frac{1}{6}\)