Question

用數(shù)學(xué)歸納法證明“4^2n-1+3ⁿ⁺¹(n∈N)能被13整除”的第二步中,當(dāng)n=k+1時(shí)為了使用歸納假設(shè),對(duì)4^2k+1+3^k+2變形正確的是(    )

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

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

Answer 1

解析：當(dāng)n=k時(shí),4^2k-1+3^k+1能被13整除,

則當(dāng)n=k+1時(shí),4^2k+1+3^k+2=4^2k-1+2+3^k+1+1=16·4^2k-1+3·3^k+1=16(4^2k-1+3^k+1)-13·3^k+1.

答案：A