How to do the second question of the synthesis of mathematical sequence and function in senior three?

(1) first proves that {an} belongs to (-1, 1), and the method is mean inequality, which is self-evident.

afterwards

Because an = 2 * (an-1)/(the square of1+an-1)

So f (an) = f (2 * (an-1)/(square of1+an-1)) =f(an- 1)+f(an- 1).

So f(an) is a geometric series with f(a 1) as the first term and 2 as the common ratio.

f(a 1)=- 1； So f(an)=- 1*(2) n- 1 power.

(2) trouble. Take a closer look.

1. First, it is proved that f(x) is odd function. Prove with f(x)+f(-x)=0, and use the formula given by the title.

2.f( 1/n * n+3n+ 1)= f( 1/n * n+3n+2- 1)= f( 1/(n+2)*(n+ 1)- 1)=-f( 1/ 1-(n+ 1)*(n+2))

=-f (n+2+(-n-1)1+(-n- 1)*(n+2)) divided by (-n-1) * (n+2).

get-f(n+2+(-n- 1)/ 1+(-n- 1)*(n+2))=-f((-n- 1)one+(n+2)

=-(f( 1/(n+2))+f( 1/(-n- 1)))=-(f( 1/(n+2))-f( 1/(n+ 1)))= f( 1/(n+ 1))-f( 1/(n+2))；

So1+f (1/5)+f (11)+...+f (1/(the square of n +3n+ 1) +f( 1/3)-f( 1/4)+.......+f( 1/n+ 1)-f( 1/n+2)+f( 1/n+2)= 1

Waiting for the best

I have written so much, I need to add more.