Question

急求一道数学题！

求证：1+1/(1*2)+1/(1*2*3)+…+1/(1*2*3*…*n)小于2

Answer 1

因为1/(1*2*3)=1/6小于1/2
1/(1*2*3*4)=1/24小于1/2
1/(1*2*3*…*n)小于1/2

所以1/(1*2*3)+…+1/(1*2*3*…*n)小于1/2
所以1+1/(1*2)+1/(1*2*3)+…+1/(1*2*3*…*n)小于1+1/2+1/2
所以1+1/(1*2)+1/(1*2*3)+…+1/(1*2*3*…*n)小于1+1
所以1+1/(1*2)+1/(1*2*3)+…+1/(1*2*3*…*n)小于2

Answer 2

因为1/(1*2*3)=1/6小于1/2
1/(1*2*3*4)=1/24小于1/2
1/(1*2*3*…*n)小于1/2

所以1/(1*2*3)+…+1/(1*2*3*…*n)小于1/2
所以1+1/(1*2)+1/(1*2*3)+…+1/(1*2*3*…*n)小于1+1/2+1/2
所以1+1/(1*2)+1/(1*2*3)+…+1/(1*2*3*…*n)小于1+1
所以1+1/(1*2)+1/(1*2*3)+…+1/(1*2*3*…*n)小于2
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