Define an operation "*" for any non-zero natural number n, which satisfies the following operation properties: (1) 1 * 1 = 1; (2) (n + 1) * 1 = 3 (n * 1). Try to find the algebraic expression of n * 1 with respect to n
Let n * 1 = an, then A1 = 1, an + 1 = 3an, {an} is an equal ratio sequence with 1 as the first term and 3 as the common ratio, {an = 3n-1, that is, n * 1 = 3n-1
RELATED INFORMATIONS
- 1. Define an operation "*": for natural number n, it satisfies the following operation properties: (I) 1 * 1 = 1, (II) (n + 1) * 1 = n * 1 + 1, then n * 1 equals () A. nB. n+1C. n-1D. n2
- 2. There is an operation program, when a ⊕ B = n (n is a constant), define (a + 1) ⊕ B = n + 1, a ⊕ (B + 1) = n-2, now known 1 ⊕ 1 = 2, then 2010 ⊕ 2010=______ .
- 3. When a ♁ B = n (n is a constant), we can get (a + 1) ♁ B = n + 1, a ♁ (B + 1) = n + 2, then (a + 2) ♁ (B + 2)= (can you talk about the process? Thank you. Thank you very much. The sooner the better.)
- 4. There is an operation program, can make a ⊕ B = n (n is a constant), get (a + 1) ⊕ B = n + 1, a ⊕ (B + 1) = n-2=______ .
- 5. There is an operation program, which can make a ⊕ B = n (n is a constant), get (a + 1) ⊕ B = n + 1, a ⊕ (B + 1) = n-2=______ .
- 6. If a ⊕ B = n (n is a constant), then (a + 1) ⊕ B = n + 1, a ⊕ (B + 1) = n-2 When a ♁ B = n (n is a constant), we can get (a + 1) ♁ B = n + 1, a ♁ (B + 1) = n-2. Now we know that 1 ♁ 1 = 2, then 2008 ♁ 2008=____
- 7. Define a kind of operation "*", for positive integer n satisfying the following operation properties: (1) 1 * 1 = 1, (2) (n + 1) * 1 = 3 (n * 1), then n * 1 is represented by an algebraic expression containing n______ .
- 8. Given that m.n are all natural numbers and m (m-n) - n (n-m) is greater than 12, find the value of M.N
- 9. It is known that m.n is a natural number (m ≠ n). What are m / 1 + n / = 1, m and N? It is known that m and N are natural numbers (m ≠ n). M / 1 + n / 2 = 1, what are m and N?
- 10. If M and N are natural numbers and M / 13 + n / 4 = 29 / 52, then M + n = ()
- 11. Is 0 a natural number? What is the concept of natural number?
- 12. Please use n for three consecutive even numbers (n is a natural number), and their sum is. Use M for two consecutive odd numbers (M is a natural number), and their sum is The two questions are irrelevant If there are three consecutive even numbers, whether there must be two consecutive odd numbers satisfying the upper number filling method, if there must be, please explain the filling method: if not, please explore and give the conditions that the number in the middle of the three consecutive even numbers must exist
- 13. All natural numbers are integers, and all integers are natural numbers______ (judge right or wrong)
- 14. How many natural numbers can be taken from 1.2.3.2004, so that the difference between each two numbers is not equal to 51005
- 15. How many natural numbers can be taken from 1, 2, 3, 2004, 2005 at most, and the difference between each two numbers is not equal to 4
- 16. Find the sum of the last two digits of M = 1! + 2! + 3! +. + 2003! + 2004
- 17. If n is a positive integer, define n! = n * (n-1) * (n-2) * 3 * 2 * 1, let m = 1! + 4! + +2006! + 2007!, then the sum of the last two digits of M is:
- 18. If n is a positive integer, define n! =n×(n-1)×(n-2)×… X 3 × 2 × 1, let m = 1! +2! +3! +4! +… +2003!+2004! Then the sum of the last two digits of M is______ .
- 19. Given that the polynomial x ^ 2 + ax-9 can be factorized in the range of integers, then the value of natural number a is 8, why should - 8 be abandoned?
- 20. If x ^ 2 + ax-9 = (x + m) (x + n) m, n is a positive integer, then the value of natural number a is? A.0, - 8.8b. Plus or minus 8 c.0, - 8 d.0,8 d.0 If x ^ 2 + ax-9 = (x + m) (x + n) n is an integer, then there is the value of natural number a? A. 0, - 8.8 B. plus or minus 8 C. - 8 d.0,8