Question

高二数学大题3，必采纳求学霸

Answer 1

解由题知an=a1+(n-1)×3=3+(n-1)×2=2n+1
则Sn=(a1+an)n/2
=(3+2n+1)n/2
=n(n+2)
则1/Sn=1/n(n+2)=1/2[1/n-1/(n+2)]
则S=1/S1+1/S2+........1/Sn
=1/2(1/1-1/3)+1/2(1/2-1/4)+1/2(1/3-1/5)+.........1/2(1/n-1/(n+2))
=1/2(1/1+1/2-1/(n+1)-1/(n+2))
=3/4-1/2(1/(n+1)(n+2))

追问

可以写出来发图吗

Answer 2

a1=3, d=2
Sn=3n+1/2*2n(n-1)=n(n+2)
1/Sn=1/n(n+2)=1/2[1/n-1/(n+2)]
S=1/2[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+...+(1/n-1/(n+2)]=1/2[1-1/(n+1)-1/(n+2)]
S=1/2[3/2-1/(n+1)-1/(n+2)]
S==(3n^2+5n)/[4(n^2+3n+2)

Answer 3

先求出Sn

追答

再用裂项的方法就可以了