实数a1,a2,…ak.他们之和为0.求证极限:lim{a1*(n+1)^(1/2)+a2*(n+2)^(1/2)+…ak*(n+k)^(1/2)}=0a1*(n+1)^(1/2)表示a1乘以n+1的1/2次方
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![实数a1,a2,…ak.他们之和为0.求证极限:lim{a1*(n+1)^(1/2)+a2*(n+2)^(1/2)+…ak*(n+k)^(1/2)}=0a1*(n+1)^(1/2)表示a1乘以n+1的1/2次方](/uploads/image/z/10441006-70-6.jpg?t=%E5%AE%9E%E6%95%B0a1%2Ca2%2C%E2%80%A6ak.%E4%BB%96%E4%BB%AC%E4%B9%8B%E5%92%8C%E4%B8%BA0.%E6%B1%82%E8%AF%81%E6%9E%81%E9%99%90%EF%BC%9Alim%7Ba1%2A%28n%2B1%29%5E%EF%BC%881%2F2%EF%BC%89%2Ba2%2A%28n%2B2%29%5E%281%2F2%29%2B%E2%80%A6ak%2A%28n%2Bk%29%5E%281%2F2%29%7D%3D0a1%2A%28n%2B1%29%5E%EF%BC%881%2F2%29%E8%A1%A8%E7%A4%BAa1%E4%B9%98%E4%BB%A5n%2B1%E7%9A%841%2F2%E6%AC%A1%E6%96%B9)
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实数a1,a2,…ak.他们之和为0.求证极限:lim{a1*(n+1)^(1/2)+a2*(n+2)^(1/2)+…ak*(n+k)^(1/2)}=0a1*(n+1)^(1/2)表示a1乘以n+1的1/2次方
实数a1,a2,…ak.他们之和为0.求证极限:lim{a1*(n+1)^(1/2)+a2*(n+2)^(1/2)+…ak*(n+k)^(1/2)}=0
a1*(n+1)^(1/2)表示a1乘以n+1的1/2次方
实数a1,a2,…ak.他们之和为0.求证极限:lim{a1*(n+1)^(1/2)+a2*(n+2)^(1/2)+…ak*(n+k)^(1/2)}=0a1*(n+1)^(1/2)表示a1乘以n+1的1/2次方
=lim[a1*(n+1)^(1/2)+a2*(n+2)^(1/2)+…+a(k-1)*(n+k-1)^(1/2)-(a1+a2+…+a(k-1))*(n+k)^(1/2)]
=lim{a1*[(n+1)^(1/2)-(n+k)^(1/2)]+a2*[(n+2)^(1/2)-(n+k)^(1/2)]+…a(k-1)*[(n+k-1)^(1/2)-(n+k)^(1/2)]}
=lim{a1*[(n+1)^(1/2)-(n+k)^(1/2)]}+lim{a2*[(n+2)^(1/2)-(n+k)^(1/2)]}+…+lim{a(k-1)*[(n+k-1)^(1/2)-(n+k)^(1/2)]}
=0+0+...+0(k个0,即可数个0)
=0
n趋近多少?????
实数a1,a2,…ak.他们之和为0.求证极限:lim{a1*(n+1)^(1/2)+a2*(n+2)^(1/2)+…ak*(n+k)^(1/2)}=0a1*(n+1)^(1/2)表示a1乘以n+1的1/2次方
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