Question

tinh tong 5^1000+5^999+5^998+...+5

 

Answer 1

Ta có: A = 5¹⁰⁰⁰ + 5⁹⁹⁹ + 5⁹⁹⁸ + ... + 5

\(\Rightarrow\)   5A = 5¹⁰⁰¹ + 5¹⁰⁰⁰ + 5⁹⁹⁹ + ... + 5²

\(\Rightarrow\)5A - A = (5¹⁰⁰¹ + 5¹⁰⁰⁰ + 5⁹⁹⁹ +... + 5²) - ( 5¹⁰⁰⁰ + 5⁹⁹⁹ + 5⁹⁹⁸ + ... + 5 )

\(\Rightarrow\)4A = 5¹⁰⁰¹ - 5

\(\Rightarrow\)A = \(\frac{5^{1001}-5}{4}\)

Answer 2

Đặt \(C=5+5^2+5^3+...+5^{998}+5^{999}+5^{1000}\)

\(\Rightarrow5C=5^2+5^3+5^4+....+5^{999}+5^{1000}+5^{1001}\)

\(\Rightarrow5C-C=\left(5^2+5^3+...+5^{1000}+5^{1001}\right)-\left(5+5^2+...+5^{999}+5^{1000}\right)\)

\(\Rightarrow4C=5^{1001}-5\)

=> C = (5¹⁰⁰¹ - 5) / 4