Can (n + 7) 2 - (N-5) 2 be divisible by 24 when n is a natural number? Give reasons
Because (n + 7) 2 - (N-5) 2 = (2n + 2) (n + 7-N + 5) = 24 (n + 1), and N is a natural number, it must be divisible by 24
RELATED INFORMATIONS
- 1. As shown in the figure, ab = AC, ad = AE, ∠ BAC = ∠ DAE
- 2. As shown in the figure, in △ ABC, ab = AC, ad is high, and am is the bisector of ∠ CAE at the outer angle of △ ABC. (1) draw the bisector DN of ∠ ADC with ruler; (2) let DN and am intersect at point F to judge the shape of △ ADF. (only write the result)
- 3. If the degree ratio of the top and bottom angles of an isosceles triangle is 2:1, what are the top and bottom angles of the triangle
- 4. An isosceles triangle, the ratio of its vertex angle to its base angle is 1:4, and its base angle is ()?
- 5. 1. The degree ratio of a base angle to a vertex angle of an isosceles triangle is 1:4, and its vertex angle is () 2. For a project, it takes 10 days for Party A to do it alone and 15 days for Party B to do it alone. The ratio of working time between Party A and Party B is (), and the ratio of working efficiency is ()
- 6. 1+3+5+97+99/2+4+6+98+100=? 1 + 3 + 5 +... + 97 + 99 / 2 + 4 + 6 +... + 98 + 100 =? It's a mistake
- 7. This is a mark problem And 1 / 21 + 202 / 2121 + 50505 / 2121 + 13131313 / 2121 1/2+3/4+5/6+… /… +97/98+99/100
- 8. 1+2+3+4+5.+95+96+97+98+99=?
- 9. 1+2+3+4+5+6+7+8.+95+96+97+98+99+100
- 10. Calculate (- 1) × (- 1) 2 × ((- 1) 3 × ×(-1)^99×(-1)^100
- 11. Sequence summation 1 + 3 + 5 +. + (2n-1)
- 12. Sum of sequence: 1 * 3 + 3 * 5 + 5 * 7 +. + (2n-1) (2n + 1)
- 13. Sum: S = 1 + 2x + 3x ^ 2 +... + NX ^ (n-1)
- 14. For real number x, use [x] to represent the largest integer not exceeding x, such as [0.32] = 0, [5.68] = 5. If n is a positive integer, an = [N4], and Sn is the sum of the first n terms of the sequence {an}, then S8=______ 、S4n=______ .
- 15. 2N-1 of the N-1 power of 2 leads to the sum of the first n terms of the formula
- 16. If a sequence is 1,3,6,10,15,21 ··· n, then the formula of the first n sum of the sequence is many?
- 17. What is the 20th of sequence 1,3,6,10,15,21 ··
- 18. Sequence summation 1 / 3 + 1 / 5 + 1 / 7 + +1/21=?
- 19. Sequence 0 + 1 + 3 + 6 + 10 What is the summation formula?
- 20. [sequence summation] 1 + 2x + 3x ^ 2 + +nx^n-1=()? 1+2*x+3*(x^2)+…… +n*x^(n-1)=( When x is not equal to 1, = (1-x ^ n) / [(1-x) ^ 2] - [n * (x ^ n)] / (1-x) When x equals 1, = n (n + x) / 2