Question

哪位大神能告诉我这道数学题怎么证明？ 试证明:

Answer 1

Answer 2

证明
原式=25×3×3^2n×2^n－36×3^n×2^n×3^n
=75×3^2n×2^n－36×3^2n×2^n
=3^2n×2^n×39
=3^2n×2^n×3×13
所以能被13 整除

Answer 3

能，3+6+5+6—6—5
=n=3

Answer 4

5^2×3^(2n+1)×2^n-3^n×6^(n+2)
=5^2×3^(2n+1)×2^n-3^n×(2×3)^(n+2)
=5^2×3^(2n+1)×2^n-3^n×2^(n+2)×3^(n+2)
=5^2×3^(2n+1)×2^n-3^(2n+2)×2^(n+2)
=5^2×3^(2n+1)×2^n-3^(2n+1)×3×2^n×2^2
=3^(2n+1)×2^n×[5^2-3×2^2]
=3^(2n+1)×2^n×[25-12]
=3^(2n+1)×2^n×13

Answer 5

证明：
原式=5^2x3^（2n+1）x2^n-2x2x3x3x3^nx3^nx2^n
=3^（2n+1）x2^nx(5^2-12)
=13x3^（2n+1）x2^n
∵3^（2n+1）为整数，2^n为整数
∴13x3^（2n+1）x2^n÷13=3^（2n+1）x2^n 为整数

希望可以帮到你。