数列2又1/3,4又1/9,6又1/27.2n+1/3^n的前N项和
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![数列2又1/3,4又1/9,6又1/27.2n+1/3^n的前N项和](/uploads/image/z/373608-0-8.jpg?t=%E6%95%B0%E5%88%972%E5%8F%881%2F3%2C4%E5%8F%881%2F9%2C6%E5%8F%881%2F27.2n%2B1%2F3%5En%E7%9A%84%E5%89%8DN%E9%A1%B9%E5%92%8C)
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数列2又1/3,4又1/9,6又1/27.2n+1/3^n的前N项和
数列2又1/3,4又1/9,6又1/27.2n+1/3^n的前N项和
数列2又1/3,4又1/9,6又1/27.2n+1/3^n的前N项和
Sn=(2+1/3)+(4+1/9)+...+(2n+1/3^n)
=(2+4+...+2n)+(1/3+1/9+1/3^n)
=(2+2n)n/2+1/3(1-1/3^n)/(1-1/3)
=(n+1)n+1/2(1-1/3^n)
=n²+n+1/2-1/[2*3^n].