用定积分定义求极限,n趋向无穷 1/(根号(4n^2-1))+1/(根号(4n^2-2^2))+…+1/(根
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用定积分定义求极限,n趋向无穷 1/(根号(4n^2-1))+1/(根号(4n^2-2^2))+…+1/(根
用定积分定义求极限,n趋向无穷
1/(根号(4n^2-1))+1/(根号(4n^2-2^2))+…+1/(根号(4n^2-n^2))
用定积分定义求极限,n趋向无穷
1/(根号(4n^2-1))+1/(根号(4n^2-2^2))+…+1/(根号(4n^2-n^2))
1/(√(4n^2-1))+1/(√(4n^2-2^2))+…+1/(√(4n^2-n^2))
=(1/n)[1/(√(4-1/n^2))+1/(√(4-2^2/n^2))+…+1/(√(4-n^2/n^2))
考虑函数f(x)=1/√(4-x^2),定义区间[0,1],分区间n等分,取右端点:
lim(1/n)[1/(√(4-1/n^2))+1/(√(4-2^2/n^2))+…+1/(√(4-n^2/n^2))
=∫(0,1)1/√(4-x^2)dx
=arcsin(x/2)|(0,1)
=π/6
=(1/n)[1/(√(4-1/n^2))+1/(√(4-2^2/n^2))+…+1/(√(4-n^2/n^2))
考虑函数f(x)=1/√(4-x^2),定义区间[0,1],分区间n等分,取右端点:
lim(1/n)[1/(√(4-1/n^2))+1/(√(4-2^2/n^2))+…+1/(√(4-n^2/n^2))
=∫(0,1)1/√(4-x^2)dx
=arcsin(x/2)|(0,1)
=π/6
用定积分定义求极限,n趋向无穷 1/(根号(4n^2-1))+1/(根号(4n^2-2^2))+…+1/(根
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