Question

[Monsieur Tuna]

A = 10 x ( 1/2 + 5/6 + 11/12 + 19/20 + ....+ 89/90 )

Đây là toán nâng cao cho HS khá giỏi nhé 
Khuyến khích mấy bn giỏi lm

Lm được cho 10 tk

Answer 1

[Lê Ng Hải Anh]

Ta có:

\(A=10\times\left(1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\right)\)

\(=10\times\left[9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\right]\)

\(=10\times\left[9-\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\right)\right]\)

\(=10\times\left[9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\right]\)

\(=10\times\left[9-\left(1-\frac{1}{10}\right)\right]\)

\(=10\times\left(9-\frac{9}{10}\right)\)

\(=10\times\frac{81}{10}\)

\(=81\)

Vậy; A = 81

=.= hk tốt!!

Answer 2

[Đức vs Hải]

☺☺