已知数列(1/1*4),(1/4*7)…,(1/(3n-2)(3n+1)),…,计算数列和S1,S2,S3,S4,根据计算结果猜想具体点,怎么求S1,S2...
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![已知数列(1/1*4),(1/4*7)…,(1/(3n-2)(3n+1)),…,计算数列和S1,S2,S3,S4,根据计算结果猜想具体点,怎么求S1,S2...](/uploads/image/z/3804646-22-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BC%881%2F1%2A4%EF%BC%89%2C%EF%BC%881%2F4%2A7%EF%BC%89%E2%80%A6%2C%EF%BC%881%2F%EF%BC%883n-2%29%283n%2B1%29%EF%BC%89%2C%E2%80%A6%2C%E8%AE%A1%E7%AE%97%E6%95%B0%E5%88%97%E5%92%8CS1%2CS2%2CS3%2CS4%2C%E6%A0%B9%E6%8D%AE%E8%AE%A1%E7%AE%97%E7%BB%93%E6%9E%9C%E7%8C%9C%E6%83%B3%E5%85%B7%E4%BD%93%E7%82%B9%2C%E6%80%8E%E4%B9%88%E6%B1%82S1%2CS2...)
已知数列(1/1*4),(1/4*7)…,(1/(3n-2)(3n+1)),…,计算数列和S1,S2,S3,S4,根据计算结果猜想具体点,怎么求S1,S2...
已知数列(1/1*4),(1/4*7)…,(1/(3n-2)(3n+1)),…,计算数列和S1,S2,S3,S4,根据计算结果猜想
具体点,怎么求S1,S2...
已知数列(1/1*4),(1/4*7)…,(1/(3n-2)(3n+1)),…,计算数列和S1,S2,S3,S4,根据计算结果猜想具体点,怎么求S1,S2...
1/1*4=(1/1-1/4)/3
1/4*7=(1/4-1/7)/3
.
1/(3n-2)(3n+1)=[1/(3n-2)-1/(3n+1)]/3
.
S1=1/1*4=(1/1-1/4)/3=1/4
S2=1/1*4+1/4*7=(1/1-1/4)/3+(1/4-1/7)/3=[1-1/4+1/4-1/7]/3=[1-1/7]/3=2/7
.
Sn=1/1*4+1/4*7+.1/(3n-2)(3n+1)
=(1/1-1/4)/3+(1/4-1/7)/3+.+[1/(3n-2)-1/(3n+1)]/3
=[1-1/4+1/4-1/7+.+1/(3n-2)-1/(3n+1)]/3
=[1-1/(3n+1)]/3
=n/(3n+1)