If the function f (x) = (m-2) x multiplied by X + (m-1) x + 2 is even, find the monotone decreasing interval of F (x + 1) and explain the reason

Because f (x) is an even function, M = 1
So f (x) = - x squared + 2
F (x + 1) = - (x + 1) square + 2
So the monotone decreasing interval is (- 1, positive infinity)

At the end of senior one in Chongqing No.1 Middle School in winter vacation 2012, we know that FX () is defined on positive integer set, and for any n ∈ n, f (f (n)) = 3N + 2, f (2) = 1, f (80) =?

f(2)=1 f(f(2))=f(1)=8 f(f(1))=f(8)=5 f(f(8))=f(5)=26 f(f(5))=f(26)=17 f(f(26))=f(17)=80 f(f(17))=f(80)=53

Calculate 3 / 1 * 4 + 3 / 4 * 7 + 3 / 7 * 10 +... + 3 / (3n-5) (3n-2) + 3 / (3n-2) (3N + 1)

3/(3n-2)(3n+1)=1/(3n-2)-1/(3n+1)
The original formula = (1 / 1-1 / 4) + (1 / 4-1 / 7) + (1 / 7-1 / 10) + +[1/(3n-2)-1/(3n+1)]
=1/1-1/4+1/4-1/7+1/7-1/10+…… +1/(3n-2)-1/(3n+1)
=1-1/(3n+1)
=3n/(3n+1)

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