Question

cho A = 1 + 1/3² + 1/3⁴ + . . . 1/3¹⁰⁰. Biết 8A = 9 - 1/3ⁿ. Vậy n =

Answer 1

A=1+1/3²+1/3⁴+.....+1/3¹⁰⁰

=>3².A=9+1/3+/3²+...+1/3⁹⁸

=>9A-A=(9+1/3+1/3²+....+1/3⁹⁸)-(1+1/3²+1/3⁴+.+1/3¹⁰⁰)

=>8A=9-1/3^100=9-1/3^n

=>1/3^100=1/3^n

=>3^100=3^n

=>n=100

Vay n=100

Answer 2

A=.............

=>\(9A=9+1+\frac{1}{3^2}+...+\frac{1}{3^{98}}\)

=>\(9A-A=\left(9+1+\frac{1}{3^2}+...+\frac{1}{3^{98}}\right)-\left(1+\frac{1}{3^2}+\frac{1}{3^4}+...+\frac{1}{3^{100}}\right)\)

=>\(8A=9-\frac{1}{3^{100}}\)

=>n=100