Question

A=\(\frac{1}{3}\)+\(\frac{2}{3^2}\)+\(\frac{3}{3^3}\)+...+\(\frac{100}{3^{100}}\)

CMR:A<\(\frac{3}{4}\)

Ai đúng và nhanh nhất mk tích nhé !

Answer 1

          A = 1/3 + 2/3² + 3/3³ + ... + 100/3¹⁰⁰ 

=>    3A = 1 + 2/3 + 3/3² + ... + 100/3⁹⁹ 

     -    A =       1/3 + 2/3² + ... + 99/3⁹⁹ + 100/ 3¹⁰⁰ 

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=>    2A = 1 + 1/3 + 1/3² + ... + 1/3⁹⁹ + 100/3¹⁰⁰ 

=>    6A = 3 + 1 + 1/3 + ... + 1/3⁹⁸ + 100/3⁹⁹ 

     -  2A = 1 + 1/3 + 1/3² + ... + 1/3⁹⁸ + 1/3⁹⁹ +100/3¹⁰⁰ 

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    4A = 3 - 99/3⁹⁹ - 100/3¹⁰⁰  <  3

=>    4A  <  3

=>    A  <  3/4