Problem: If s=⎝⎛1+2−321⎠⎞⎝⎛1+2−161⎠⎞⎝⎛1+2−81⎠⎞⎝⎛1+2−41⎠⎞⎝⎛1+2−21⎠⎞, then s is equal to
Answer Choices:
A. 21⎝⎛1−2−321⎠⎞−1
B. ⎝⎛1−2−321⎠⎞−1
C. 1−2−321
D. 21⎝⎛1−2−321⎠⎞
E. 21
Solution:
Let x=2−321. Then s=(1+x)(1+x2)(1+x4)(1+x8)(1+x16)
Now (1−x)s=1−x32=21. ∴s=21(1−x)−1=21⎝⎛1−2−321⎠⎞−1