Question

Tính T , biết :

\(T=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+...+\frac{89}{90}+\frac{109}{110}+\frac{10}{11}.\)

 

Answer 1

T = \(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+...+\frac{109}{110}+\frac{10}{11}\)

T = \(\frac{10}{11}+\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+...+\left(1-\frac{1}{110}\right)\)

T = \(\frac{10}{11}+\left(1+1+...+1\right)+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)

T = \(\frac{10}{11}+10+\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)

T = \(\frac{120}{11}+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)

T = \(\frac{120}{11}-\left(1-\frac{1}{11}\right)\)

T = \(\frac{120}{11}-\frac{9}{11}\)

T = \(\frac{111}{11}\)

Answer 2

bài của bạn Giang tính nhầm bước thứ hai từ cuối lên

Sửa: T = \(\frac{120}{11}-\frac{10}{11}=10\)