2. 1+2+3+...+n = n(n+ 1)/2 = = = & gt； 1/(1+2+3+...+n) = 2/[n (n+1)] = 2/n-2/(n+1) = = > Original formula = 2n/(.

4.bn=an+ 1-an，b 1 = a2-a 1 = 2-4 =-2 B2 = a3-a2 = 1-2 =- 1 B2-b 1 =- 1-(-2)= 1 = d

bn =-2+(n- 1)= n-3 = = = & gt； bn- 1=n-4

a2-a 1=b 1

a3-a2=b2

a4-a3=b3

...........

An-An- 1 = bn- 1 = = " An-a 1 = b 1+B2+B3+...+BN- 1 = (N- 1)()

=(n- 1)(n-6)/2 = = = & gt； an = a 1+(n- 1)(n-6)/2 = = = & gt； an=4+(n- 1)(n-6)/2

6. a 2b 2 =1,= = & gtab =1or ab =-1/a+1/b = 2 = = > a+b = 2ab = a^2+2ab+b^2=4a^2b^2=4===>； a^2+b^2=4-2ab

(a+b)/(a^2+b^2)=2ab/(4-2ab)===>； The original formula = 1 or-1/3.