已知角θ的终边经过点P(-x,-6),且cosθ=-,则sinθ=____________,tanθ=____________.
若角θ同时满足sinθ<0且tanθ<0,则角θ的终边一定落在第________象限.
设数列{an}:1,-2,-2,3,3,3,-4,-4,-4,-4,…,(-1)k-1k,…,(-1),即当(k∈N*)时,an=(-1)k-1k,记Sn=a1+a2+…+an(n∈N*),用数学归纳法证明Si(2i+1)=-i(2i+1)(i∈N*).
设函数f(x)=x-xlnx,数列{an}满足0<a1<1,an+1=f(an).求证:
(1)函数f(x)在区间(0,1)是增函数;
(2)an<an+1<1.
用数学归纳法证明不等式:>1(n∈N*且n>1).
用数学归纳法证明“12+22+32+…+n2=n(n+1)(2n+1)(n∈N*)”,当n=k+1时,应在n=k时的等式左边添加的项是________.