Question

Cho T = 5+5²+5³+....+5²⁰⁰⁰. Tìm  số tự nhiên N sao cho 4xT+5=5m

Answer 1

\(T=5+5^2+5^3+...+5^{2000}\)

=>\(5T=5^2+5^3+5^4+...+5^{2001}\)

=>\(5T-T=5^2+5^3+...+5^{2001}-5-5^2-...-5^{2000}\)

=>\(4T=5^{2001}-5\)

=>\(4T+5=5^{2001}\)

Sửa đề:\(4T+5=5^m\)

=>\(5^m=5^{2001}\)

=>m=2001

Answer 2

T=5+5²+5³+...+5²⁰⁰⁰

=>5T=5²+5³+5⁴+...+5²⁰⁰¹

=>5T−T=5²+5³+...+5²⁰⁰¹−5−5²−...−5²⁰⁰⁰

=>4T=5²⁰⁰¹−5

=>4T+5=5²⁰⁰¹

Ta có:

=>5²⁰⁰¹=5m

=>m=2001

Vậy m=2001