数列1/1×4,1/4×7,1/7×10,1/(3n-2)×(3n+1)的前n项和
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数列1/1×4,1/4×7,1/7×10,1/(3n-2)×(3n+1)的前n项和
是一个选择题A:3n/3n+1 B:n/3n+1 C:n-1/3n-2 D:3n-3/3n-2
是一个选择题A:3n/3n+1 B:n/3n+1 C:n-1/3n-2 D:3n-3/3n-2
![数列1/1×4,1/4×7,1/7×10,1/(3n-2)×(3n+1)的前n项和](/uploads/image/z/11737596-12-6.jpg?t=%E6%95%B0%E5%88%971%2F1%C3%974%2C1%2F4%C3%977%2C1%2F7%C3%9710%2C1%2F%283n%EF%BC%8D2%29%C3%97%283n%EF%BC%8B1%29%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C)
1/(3n-2)×(3n+1)=1/3*[1/(3n-2)-1/(3n+1)]
故:1/1×4,1/4×7,1/7×10,1/(3n-2)×(3n+1)的前n项和是:
1/3[1-1/4+1/4-1/7+1/7-1/10+...+1/(3n-2)-1/(3n+1)]
=1/3[1-1/(3n+1)]
=n/(3n+1)
选 B
故:1/1×4,1/4×7,1/7×10,1/(3n-2)×(3n+1)的前n项和是:
1/3[1-1/4+1/4-1/7+1/7-1/10+...+1/(3n-2)-1/(3n+1)]
=1/3[1-1/(3n+1)]
=n/(3n+1)
选 B
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