52. The total power is to the 5th. So there are 6 terms.
57. The question itself is not particularly hard to cross-multiply. 11*55, 7*89, and 89*11 all have fast shortcuts. The answer is 18/979, which roused my suspicion because 11+7=18.
After further investigation, I conclude:
b/a - (nb-1)/(na+1) = (a+b)/(a(na+1)), where, in this case, a=11, b=7, and n=8.
