Question

so sánh:

p= 1+3+3²+.....+3²⁰⁰ và Q=3²⁰¹

Answer 1

Ta có p = [ ( 3 + 3² + 3³ + ... + 3²⁰¹ ) - ( 1 + 3 + 3² + ... + 3²⁰⁰ ) ] : 2

=> p = ( 3²⁰¹ - 1 ) : 2

Vì ( 3²⁰¹ - 1 ) : 2 < 3²⁰¹ nên p < Q

Answer 2

Ta có :

\(P=1+3+3^2+3^3+...+3^{200}\)

=> \(3P=3+3^2+3^3+3^4+...+3^{201}\)

=> \(3P-P=\left(3+3^2+3^3+...+3^{201}\right)-\left(1+3+3^2+...+3^{200}\right)\)

=> \(2P=3^{201}-1\)

Ta có :  3²⁰¹ - 1 < 3²⁰¹  =>  2P < Q => P < Q