求解高等数学题上填空第一题!
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求解高等数学题上填空第一题!
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1 原式= 1/(1*2)+1/(2*3)+1/(3*4)+.+1/[n(n+1)]+ .
= 1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n+1)+.= 1
再问: 还有极限符号lim和右上角的n次方呢
再答: 重答如下:
原式 = lim {1/(1*2)+1/(2*3)+1/(3*4)+......+1/[n(n+1)]}^n
= lim [ 1-1/2+1/2-1/3+1/3-1/4+......+1/n-1/(n+1)]^n
= lim [ 1-1/(n+1)]^n
= lim{ [1-1/(n+1)]^[-(n+1)]}^[-n/(n+1) ]
= e^[ lim [ -n/(n+1)] = e^(-1) = 1/e
= 1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n+1)+.= 1
再问: 还有极限符号lim和右上角的n次方呢
再答: 重答如下:
原式 = lim {1/(1*2)+1/(2*3)+1/(3*4)+......+1/[n(n+1)]}^n
= lim [ 1-1/2+1/2-1/3+1/3-1/4+......+1/n-1/(n+1)]^n
= lim [ 1-1/(n+1)]^n
= lim{ [1-1/(n+1)]^[-(n+1)]}^[-n/(n+1) ]
= e^[ lim [ -n/(n+1)] = e^(-1) = 1/e