Question

tính nhanh:

\(A=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+\frac{1}{336}+.....+\frac{1}{496.501}\)

Answer 1

1A  = 1/6 . (1 - 1/501) = 1/6 . 500/501 => A = 500/501.6=500/3006

Answer 2

=1/1*6+1/6*11+1/11*16+1/16*31+...+1/496+1/496*501

=1/5*(1-1/6*1/6-1/11+1/11-1/16+1/16-1/31+...+1/496-1/501)

=1/5*(1-1/501)

=1/5*500/501

=100/101

Vậy A=100/101

Answer 3

giải chi tiết thêm giúp mình được ko ạ

Answer 4

Xin lỗi vì mik k bt cách viết phân số nhé,mong cậu thông cảm,mik thay bằng dấu gạch chéo nhé !

A= 1/6+1/66+1/176+1/336+...+1/496.501

A= 1/1.6+1/6.11+1/11.16+1/16.21+...+1/496.501

A=1/5.5/1.6+1/5.5/6.11+1/5.5/11.16+1/5.5/16.21+...+1/5.5/496.501

A= 1/5.(5/1.6+5/6.11+5/11.16+5/16.21+...+5/496.501

Áp dụng 1/n.1/n+1=1/n.(n+1),ta có:

A= 1/5.( 1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+...+1/496-1/501)

A= 1/5.(1-1/501)

A= 1/5.500/501

A= 1.5.100/5.501

A=100/501

mik nha !

Answer 5

=1/1*6+1/11*6+1/11*16+1/16*21+...+1/496*501

=1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+...+1/496-1/501

=1-1/501

=500/501