【最新】高中数学-高二数学2.5.2 数列求和.docx

课时训练14数列求和一、分组求和1.若数列an的通项公式是an=(-1)n(3n-2),则a1+a2+a10=()A.15B.12C.-12D.-15答案:A解析:an=(-1)n(3n-2),则a1+a2+a10=-1+4-7+10-25+28=(-1+4)+(-7+10)+(-25+28)=35=15.2.已知数列an满足a1=1,an+1=an+n+2n(nN*),则an为()A.n(n-1)2+2n-1-1B.n(n-1)2+2n-1C.n(n+1)2+2n+1-1D.n(n-1)2+2n+1-1答案:B解析:an+1=an+n+2n,an+1-an=n+2n.an=a1+(a2-a1)+(a3-a2)+(an-an-1)=1+(1+2)+(2+22)+(n-1)+2n-1=1+1+2+3+(n-1)+(2+22+2n-1)=1+(n-1)n2+2(1-2n-1)1-2=n(n-1)2+2n-1.