Question

CMR:với n nguyên dương ta có:

S=3ⁿ⁺²-2ⁿ⁺²+3ⁿ-2ⁿ  chia hết cho 10

Answer 1

S = 3ⁿ⁺² - 2ⁿ⁺² + 3ⁿ - 2ⁿ 

S = 3ⁿ.(3²+1) - 2ⁿ.(2²+1)

S = 3ⁿ. 10 - 2ⁿ.5

S = 3ⁿ . 10 - 2^n-1 . 2 . 5

S = 3ⁿ . 10 - 2^n-1 . 10

S = 10. ( 3ⁿ - 2^n-1)

=> S chia hết cho 10

Answer 2

S=3ⁿ⁺²+3ⁿ-(2ⁿ⁺²+2ⁿ)=3ⁿ(3²+1)-2ⁿ(2²+1)=3ⁿ*10-2^n-1*2*5=3ⁿ*10-2^n-1*10 chc 10