1、
f(x)=cosx+sinx=√2sin(x+π/4)
∵x∈[0,π]
∴x+π/4∈[π/4,5π/4]
∴值域为[-1,√2]
2、
b(n+1)-bn=a(n+1)+a(n+2)-an-a(n+1)
=a(n+2)-an
∵｛an}是等差数列,设公差为d
则a(n+2)-an=2d
所以数列｛bn}是等差数列