- 等比数列{an}中,a3=6,前三项和S3=∫034xdx则公比q的值为( )A.1B.-12C.1或-12D.-1或-12
- 在等比数列{an}中,a1=23,a4=∫41(1+2x)dx,则数列{an}的前5项之和的值为______.
- 已知函数f(x)=lnx-x+1(x∈[1,+∞)),数列{an}满足a1=e,=e(n∈N*), (Ⅰ)求数列{an}的通项公式an;(Ⅱ)求f(a1)+f(a2...
- 等比数列{an}的首项a1=-1,前n项和为Sn,若S10S5=3132则limn→∞Sn等于( )A.23B.-23C.2D.-2
- 若数列{an}满足:a1=13,且对任意正整数m,n都有am+n=am•an,则limn→+∞(a1+a2+…+an)=( )A.12B.23C.32D.2
- limn→∞2n1+2+22+…+2n的值是______.
- limn→∞(1+13+132+…+13n)=( )A.53B.32C.2D.不存在
- 设首项为1,公比为q(q>0)的等比数列的前n项之和为Sn,又设Tn=SnSn+1,n=1,2,….求limn→nTn.
- limn→∞3+32+…+3n3n-2n=______.
- limn→∞(12+14+…+12n)=______.
- 已知函数f(x)=3x2+bx+1是偶函数,g(x)=5x+c是奇函数,数列{an}满足an>0,且a1=1,f(an+an+1)-g(an+1an+an2)=1.(1...
- 设首项为a,公差为d的等差数列前n项的和为An,又首项为a,公比为r的等比数列前n项和为Gn,其中a≠0,|r|<1.令Sn=G1+G2+…+Gn...
- 已知数列{an}的首项a1≠0,其前n项的和为Sn,且Sn+1=2Sn+a1,则limn→∞anSn=( )A.0B.12C.1D.2
- 给出下列命题:(1)常数列既是等差数列,又是等比数列;(2)实数等差数列中,若公差d<0,则数列必是递减数列;(3)实数等...
- 等比数列{an}中,公比q>0,若limn→∞(a1+a2+…+an)=1,则a1的取值范围为______.