The Other Art of Number

Please check and think about the numbers below. There is some *arts* to make the mathematics are beautiful. The limits of quarter whit exponential 1 and etc, will reach 1/3. 1/3 will reach 1/2, 1/2 will reach 1/1. So, Please note it whit th

1. (1/4)¹ + (1/4)² + (1/4)³ + (1/4)⁴ + (1/4)⁵ + . . . . = (1/4)+(1/16)+(1/64)+(1/256)+… ≈ 1/3

   

2. (1/3)¹ + (1/3)² + (1/3)³ + (1/3)⁴ + (1/3)⁵ + . . . . = (1/3)+(1/9)+(1/27)+(1/81)+… ≈ 1/2
   
3. (1/2)¹ + (1/2)² + (1/2)³ + (1/2)⁴ + (1/2)⁵ + . . . . = (1/2)+(1/4)+(1/8)+(1/16)+… ≈ 1/1 ≈ 1