Try to explain: for any natural number n, the value of n (n + 5) - (n-3) (n + 2) can be divided by 6

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• 1. Known: known 1 + 3 = 4 = 2,1 + 3 + 5 = 9 = 3,1 + 3 + 5 + 7 = 16 = 4, then 1 + 3 + 5 + + (2n + 1) = (n + 1) 1+3+5+… +(2n + 1) how to see that there are n + 1 items, list a process for me to see
• 2. Given the first n terms of the sequence {an} and Sn = n ^ 2 + 2n (1), find the general term formula of the sequence {an} (2), find the 10th term of the sequence
• 3. The general term formula of sequence is 2n ^ 2-2n + 1, and the sum of the first n terms can be obtained
• 4. A 1 = 3, a (n + 1) = 3an - 2 fast
• 5. Given A1 = 1, a (n + 1) = 3an + 2 ^ (n + 1), find the general term formula of sequence {an}
• 6. It is known that the sum of the first n terms of the sequence is Sn = - 3 / 2n square + 205 / 2n 1, find the general term formula, 2, find the sum of the first n terms TN
• 7. Given the sum of the first n terms of the sequence {an} Sn = - 3 / 2n & sup2; + 205 / 2n, find the general term formula of the sequence {an}
• 8. Given that the sum of the first n terms of sequence {an} is Sn = 2n-3, then the general term formula of sequence a is (2n, n is above)
• 9. Given the first n terms and Sn = 3 (3 ^ n + 1) / 2 of the sequence, find its general term formula
• 10. Given the sum of the first n terms of the sequence an, Sn = an + n & # 178; - 1 (n ∈ n *) find the general term formula of the sequence an (1) (2) if BN = 1 / ana (n + 1), find the sum of the first n terms of the sequence BN
• 11. Can (n + 7) 2 - (N-5) 2 be divisible by 24 when n is a natural number? Give reasons
• 12. Using description method to express the set divided by 3 and remaining 2
• 13. Write positive odd set, odd set and integer set divisible by 3 by description
• 14. The set of all numbers divisible by 5 is represented by description
• 15. To express "a set of positive integers divided by three and remaining one" by descriptive method:______ ．
• 16. The following sets {1,3,5,7,... Are represented by description An integer divisible by 3
• 17. If n is a positive integer, and N can be divided by 5, and N can be divided by 5, then n=
• 18. Let n be a natural number, then the odd number is expressed as______ , even numbers expressed as______ The number divisible by 5 is______ The number of 3 divided by 4 is______ ．
• 19. Proof: the sum of any five consecutive integers can be divided by 5
• 20. Let y = e Λ 1 / x + sin2x, find dy