Question

用數學歸納法證明“4^2n-1+3ⁿ⁺¹(n∈N+)能被13整除”的第二步中，當n＝k+1時為了使用歸納假設，對4^2k+1+3^k+2變形正確的是

1. A.
   16(4^2k-1+3^k+1)-13×3^k+1
2. B.
   4×4^2k+9×3^k
3. C.
   (4^2k-1+3^k+1)+15×4^2k-1+2×3^k+1
4. D.
   3(4^2k-1+3^k+1)-13×4^2k-1

Answer 1

A
4^2k+1+3^k+2＝16×4^2k-1+3^k+2＝16(4^2k-1+3^k+1)+3^k+2-16×3^k+1＝16(4^2k-1+3^k)-13×3^k+1．