Question

若f(n)=2+2^4+2^7+2^10+…+2^3n+10(n属于正整数),则f(n)=?

Answer 1

设An = 2^(3n + 10)

则An是等比数列,公比q = 8

所以Sn = 2^13 + 2^16 +...+ 2^(3n + 10) = 2^13 *(1-8^n)/(1-8) = 2^13 *(8^n -1)/7

所以f(n) = Sn + 2+2^4+2^7+2^10 = 2^13 *(8^n -1)/7 + 1170