數學問題集(40)---計算題

Let1+(1/3)+(2/9) +(4/27)+(8/81)+..... ....... = n

[ 1 + ( 1 / 3 ) + ( 2 / 9 ) + ( 4 / 27 ) + ( 8 / 81 ) + ... ... ] ( 2 / 3 ) = ( 2 / 3 ) n

( 2 / 3 ) n = ( 2 / 3 ) + ( 2 / 9 ) + ( 4 / 27 ) + ( 8 / 81 ) ...

n - ( 1 / 3 ) n = ( 2 / 3 ) + ( 2 / 9 ) + ( 4 / 27 ) + ( 8 / 81 ) ...

( 1 / 3 ) n = [ 1 + ( 1 / 3 ) + ( 2 / 9 ) + ( 4 / 27 ) + ( 8 / 81 ) + ... ... ] - [ ( 2 / 3 ) + ( 2 / 9 ) + ( 4 / 27 ) + ( 8 / 81 ) ...

( 1 / 3 ) n = ( 2 / 3 )

n = 2

Answer : 1 + ( 1 / 3 ) + ( 2 / 9 ) + ( 4 / 27 ) + ( 8 / 81 ) +... ... = 2