数列{an}满足a1=1,an+1-an=n, 求该数列的通项公式an(下标不能打,可查看图片)
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![数列{an}满足a1=1,an+1-an=n, 求该数列的通项公式an(下标不能打,可查看图片)](/uploads/image/z/14296019-59-9.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D1%2Can%2B1-an%3Dn%2C+%E6%B1%82%E8%AF%A5%E6%95%B0%E5%88%97%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fan%28%E4%B8%8B%E6%A0%87%E4%B8%8D%E8%83%BD%E6%89%93%2C%E5%8F%AF%E6%9F%A5%E7%9C%8B%E5%9B%BE%E7%89%87%EF%BC%89)
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数列{an}满足a1=1,an+1-an=n, 求该数列的通项公式an(下标不能打,可查看图片)
数列{an}满足a1=1,an+1-an=n, 求该数列的通项公式an(下标不能打,可查看图片)
数列{an}满足a1=1,an+1-an=n, 求该数列的通项公式an(下标不能打,可查看图片)
因为an+1-an=n 则a2-a1=1 a2=a1+1=2
且an-a(n-1)=n-1 (括号内为下标)
a(n-1)-a(n-2)=n-2
.
a2-a1=1
上述式子相加得
an-a1=n(n-1)/2
所以an=n(n-1)/2+1
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