作业帮数列1/(2*5) 1/(5*8) 1/(8*11)……1/[(3n_1)(3n+2)]的前几项和=___________我老师出了点方法,我就算到1/3[1/(3n-1)-1/(3n+2)]1/3(1/2-1/5)+1/3(1/5-1/8)+1/3……1/3[1/(3n-1)-1/(3n+2)]1/3[1/2-1/5+1/5-1/8+1/8-……+1/(3n-1)-1/(3n+2)]1/3[1/
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![数列1/(2*5) 1/(5*8) 1/(8*11)……1/[(3n_1)(3n+2)]的前几项和=___________我老师出了点方法,我就算到1/3[1/(3n-1)-1/(3n+2)]1/3(1/2-1/5)+1/3(1/5-1/8)+1/3……1/3[1/(3n-1)-1/(3n+2)]1/3[1/2-1/5+1/5-1/8+1/8-……+1/(3n-1)-1/(3n+2)]1/3[1/](/uploads/image/z/1767793-49-3.jpg?t=%E6%95%B0%E5%88%971%2F%282%2A5%29+1%2F%285%2A8%29+1%2F%288%2A11%29%E2%80%A6%E2%80%A61%2F%5B%283n_1%29%283n%2B2%29%5D%E7%9A%84%E5%89%8D%E5%87%A0%E9%A1%B9%E5%92%8C%3D___________%E6%88%91%E8%80%81%E5%B8%88%E5%87%BA%E4%BA%86%E7%82%B9%E6%96%B9%E6%B3%95%2C%E6%88%91%E5%B0%B1%E7%AE%97%E5%88%B01%2F3%5B1%2F%283n-1%29-1%2F%283n%2B2%29%5D1%2F3%281%2F2-1%2F5%29%2B1%2F3%281%2F5-1%2F8%29%2B1%2F3%E2%80%A6%E2%80%A61%2F3%5B1%2F%283n-1%29-1%2F%283n%2B2%29%5D1%2F3%5B1%2F2-1%2F5%2B1%2F5-1%2F8%2B1%2F8-%E2%80%A6%E2%80%A6%2B1%2F%283n-1%29-1%2F%283n%2B2%29%5D1%2F3%5B1%2F)
数列1/(2*5) 1/(5*8) 1/(8*11)……1/[(3n_1)(3n+2)]的前几项和=___________我老师出了点方法,我就算到1/3[1/(3n-1)-1/(3n+2)]1/3(1/2-1/5)+1/3(1/5-1/8)+1/3……1/3[1/(3n-1)-1/(3n+2)]1/3[1/2-1/5+1/5-1/8+1/8-……+1/(3n-1)-1/(3n+2)]1/3[1/
数列1/(2*5) 1/(5*8) 1/(8*11)……1/[(3n_1)(3n+2)]的前几项和=___________
我老师出了点方法,我就算到
1/3[1/(3n-1)-1/(3n+2)]
1/3(1/2-1/5)+1/3(1/5-1/8)+1/3……1/3[1/(3n-1)-1/(3n+2)]
1/3[1/2-1/5+1/5-1/8+1/8-……+1/(3n-1)-1/(3n+2)]
1/3[1/2-1/(3n+2)=___?_____
接下来怎么算啊?给个详解,就从1/3[1/2-1/(3n+2)=___?_____这个开始算给我吧!
数列1/(2*5) 1/(5*8) 1/(8*11)……1/[(3n_1)(3n+2)]的前几项和=___________我老师出了点方法,我就算到1/3[1/(3n-1)-1/(3n+2)]1/3(1/2-1/5)+1/3(1/5-1/8)+1/3……1/3[1/(3n-1)-1/(3n+2)]1/3[1/2-1/5+1/5-1/8+1/8-……+1/(3n-1)-1/(3n+2)]1/3[1/
an=1/[(3n-1)(3n+2)]=(1/3)*[1/(3n-1)-1/(3n+2)]
那么Sn=a1+a2+...+an
=(1/3)*(1/2-1/5)+(1/3)*(1/5-1/8)+...+(1/3)*[1/(3n-1)-1/(3n+2)]
=(1/3)*[1/2-1/(3n+2)]
=(1/3)*[(3n+2-2)/2(3n+2)](通分)
=n/2(3n+2)
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