已知等差数列{an}的公差为2,其前n项和Sn=pn²+2n(n∈N*).
(I)求p的值及an;
(II)若bn=2/﹙2n-1﹚an,记数列{bn}的前n项和为Tn,求使Tn﹥9/10成立的最小正整数n的值
(I)∵{an}的等差数列
∴Sn=na1+n(n-1)d/2=na1+n(n-1)=n²+(a1-1)n
又由已知Sn=pn²+2n,
∴p=1,a1-1=2,
∴a1=3,
∴an=a1(n-1)d=2n+1
∴p=1,an=2n+1;
(II)由(I)知bn=2/(2n-1)(2n+1)=1/(2n-1)-1/(2n+1)
∴Tn=b1+b2+b3+…+bn
=(1-1/3)+(1/3-1/5)+(1/5-1/7)+……+[1/(2n-1)-1/(2n+1)]
=1-1/(2n+1)
=2n/(2n+1)
∵Tn>9/10
∴2n/(2n+1)>9/10,解得 n>9/2 又∵n∈N+
∴n=5