Câu hỏi của nguyenminhquan

Question

tính: A= 1/2 +5/6 + 11/12 + 19/20 + 29/30 + 4142 + 55/56 + 71/82 + 89/90 + 109/110

Nguyễn Lê Phước Thịnh · Accepted Answer

Sửa đề: $A=\frac12+\frac56+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}+\frac{109}{110}$

$=1-\frac12+1-\frac16+1-\frac{1}{12}+1-\frac{1}{20}+\cdots+1-\frac{1}{110}$

$=10-\left(\frac12+\frac16+\frac{1}{12}+\cdots+\frac{1}{110}\right)$

$=10-\left(1-\frac12+\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{10}-\frac{1}{11}\right)$

$=10-\left(1-\frac{1}{11}\right)=10-\frac{10}{11}=\frac{110}{11}-\frac{10}{11}=\frac{100}{11}$

Câu trả lời:

Sửa đề: $A=\frac12+\frac56+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}+\frac{109}{110}$

$=1-\frac12+1-\frac16+1-\frac{1}{12}+1-\frac{1}{20}+\cdots+1-\frac{1}{110}$

$=10-\left(\frac12+\frac16+\frac{1}{12}+\cdots+\frac{1}{110}\right)$

$=10-\left(1-\frac12+\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{10}-\frac{1}{11}\right)$

$=10-\left(1-\frac{1}{11}\right)=10-\frac{10}{11}=\frac{110}{11}-\frac{10}{11}=\frac{100}{11}$