一、选择题
1.在数列{an}中,an=1-12+13-14+…+12n-1-12n,则ak+1=( )
A.ak+12k+1 B.ak+12k+2-12k+4
C.ak+12k+2 D.ak+12k+1-12k+2
解析:ak+1=1-12+13-14+12k-1-12k+12k+1-12k+2=ak+12k+1-12k+2,故选D.
答案:D
2.已知n为正整数用数学归纳法证明f(n)=1+3+5+…+(2n-1)=n2时,假设n=k(k∈N*)时命题为真,即f(k)=k2成立,则当n=k+1时,需要用到的f(k+1)与f(k)之间的关系式是( )
A.f(k+1)=f(k)+2k-3
B.f(k+1)=f(k)+2k-1
C.f(k+1)=f(k)+2k+1
D.f(k+1)=f(k)+2k+3
解析:因为f(n)=1+3+5+…+(2n-1),
所以f(k)=1+3+5+…+(2k-1),
f(k+1)=1+3+5+…+(2k-1)+(2k+1),
所以f(k+1)=f(k)+2k+1,故选C.
答案:C