Problem: A line initially 1 inch long, grows according to the following law, where the first term is the initial length.
1+412+41+1612+161+6412+641+….
If the growth process continued forever, the limit of the length of the line is:
Answer Choices:
A. ∞
B. 34
C. 38
D. 31(4+2)
E. 32(4+2)
Solution:
Rearrange the terms:
S1=1+41+161+⋯=34 and S2=42+162+642+⋯=32∴S=S1+S2=31(4+2).