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The sum of the first n items of the arithmetic sequence is a, the sum from the N + 1 to the 2n items is B, and the sum from the 2n + 1 to the 3N items is C. (1) the known tolerance is D, and D is b-a (2) Prove that a, B and C are equal difference sequence
（1）B-A=n²d
(2)A=a1+（n-1）d
B=an+1+（n-1）d
C=a2n+1+(n-1)d
B=(A+C)/2
So it's an arithmetic sequence
Given that the function f (x) is differentiable and N is a natural number, what is LIM (n → 0) n [f (x + 1 / N) - f (x)] equal to
N is a natural number, how is n - > 0?
Should it be n -- > ∞?
In this way:
lim(n→∞) n[f(x+1/n)-f(x)]=lim(n→∞) [f(x+1/n)-f(x)]/(1/n)=f'(x)
When x is a natural number not equal to o, f (n) is also a natural number not equal to 0, and f (f (n)) = 3N
When x is a natural number not equal to o, f (n) is also a natural number not equal to 0, and f (f (n)) = 3N, then the value of F (5) =?
F (f (n)) = 3N, ｜ f (f (1)) = 3, and f (1) ≠ 1 ∵ f (x) ∈ n*
∴f(1)≥2
∵ f (x) is a monotone increasing function over 0
∴f(2)≤f(f(1))=3
∴f(3)≥f(f(2))=6
∴f(6)≤f(f(3))=9
∴f(1)=2,f(2)=3,f(3)=6,f(4)=7,f(5)=8
∴f(5)=8
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