Question

Chứng minh rằng :

\(\frac{1}{7^2}\)- \(\frac{1}{7^4}\)+........+ \(\frac{1}{7^{4n-2}}\)- \(\frac{1}{7^{4n}}\) +.......+\(\frac{1}{7^{98}}\)- \(\frac{1}{7^{100}}\)< \(\frac{1}{50}\)

 

Answer 1

\(A=\frac{1}{7^2}-\frac{1}{7^4}+...+\frac{1}{7^{98}}-\frac{1}{7^{100}}\)

\(7^2.A=1-\frac{1}{7^2}+\frac{1}{7^4}-...+\frac{1}{7^{100}}-\frac{1}{7^{102}}\)

\(\Rightarrow49A+A=1-\frac{1}{7^{102}}

Answer 2

Ta đặt : A = 1/7 2 - 1/7 4  + ... + 1/7 9s - 1/7 100

=> : A = 1 - 1/7 2 + 1/7 4 -... + 1/7 100 - 1/7 102

=< : 49 + 4 = 1 - 1/7 102 < 1

<=>  : 50A < 1 => 1/50

 mk biết rõ lun