等差数列公差为2,前n项和Sn=Pn方+2n若bn=﹙2n-1﹚An分之2,记数列{Bn}的前N项和为Tn,求使Tn﹥1

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  • 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