There is a circle. For the first time, a diameter is used to divide the circle into two half circles, and 1 is marked on each point; for the second time, the two half circles are divided into two (1/4) circles respectively, and in Mark (1/2) of the sum of two adjacent numbers on the newly generated subpoint; for the third time, divide the four (1/4) circles into two (1/8) circles respectively, and add Mark the sum of two adjacent numbers (1/3) on the division point; for the fourth time, divide the eight (1/8) circles into two (1/16) circles respectively, and on the newly generated division point Mark (1/4) the sum of two adjacent numbers...and do this 100 times. May I ask: What is the sum of all the numbers on the last circle?
有一个圆，第一次用一条直径将圆周分成两个半圆周，在每个分点上标上1；第二次，再将两个半圆周分别分成两个(1/4)圆周，在新产生的分点上标上相邻两数之和的(1/2)；第三次，再将四个(1/4)圆周分别分成两个(1/8)圆周，在新产生的分点上标上相邻两数之和的(1/3)；第四次，再将八个(1/8)圆周分别分成两个(1/16)圆周，在新产生的分点上标上相邻两数之和的(1/4)…如此进行了100次．请问：最后圆周上的所有数之和是多少？
<gadget id="calculator">100 + 2</gadget>
<output>102</output>

<gadget id="calculator">100 + 1</gadget>
<output>101</output>

<gadget id="calculator">102 * 101</gadget>
<output>10_302</output>

<gadget id="calculator">10_302 / 3</gadget>
<output>3_434</output>

<result>3_434</result>