A<1-1/2+1/2-1/3+...+1/8-1/9=1-1/9=8/9

A>1/2-1/3+1/3-1/4+...+1/9-1/10=1/2-1/10=2/5

=>2/5<A<8/9

\(A=3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+..+\frac{3}{2^9}\)

\(2A=6+3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^8}\)

\(2A-A=\left[6+3+\frac{3}{2}+...+\frac{3}{2^8}\right]-\left[3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right]\)

=> A = 6 + 3/2^9 = 3075/512

Mik ghi nhầm, thay A bằng S giùm nha

Cảm ơn

Học giỏi nhé pạn

mong bn lan sau vt de hiu hon!please

S=3 + 3/2 + (3/2)² + ... + (3/2)⁹

(3/2).S= 9/2 + (3/2)² + (3/2)³ + ... +(3/2)¹⁰

(3/2).S-S=[ 9/2 + (3/2)² + (3/2)³ + ... +(3/2)¹⁰ ] - [3 + 3/2 + (3/2)² + ... + (3/2)⁹ ]

(1/2).S=(9/2 -3)+[(3/2)¹⁰ - (3/2)]

S= 3 + (3/2)¹⁰ - 3

S= (3/2)¹⁰

Đề bài yêu cầu j vậy?

mũ 2 tui ko bt

chịu bạn ơi

a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)

 1/2 x 2 mũ n cộng 4 x 2 mũ n = 9 x 2 mũ n