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The second question is how to do it. Math problems in college entrance examination. 20 14 national volume 2.
3^n- 1=3*3^(n- 1)- 1=2*3^(n- 1)+[3^(n- 1)- 1]≥2*3^(n- 1)+0=2*3^(n- 1)

So,

1/an≤[ 1/3^(n- 1)]

( 1/a 1)+( 1/a2)+.......+( 1/an)≤ 1+( 1/3)+( 1/3^2)+.....+[ 1/3^(n- 1)]=[ 1/( / kloc-0/- 1/3)[ 1-( 1/3)^n]<; [ 1/( 1- 1/3)][ 1-0]=3/2

So,

( 1/a 1)+( 1/a2)+.......+( 1/an)& lt; 3/2