Question

tìm n biết

2/3+2/15+2/35+..........+2/n=322/323

Dấu / là gạch phân số.

Answer 1

2/3 + 2/15 + 2/35 + ... + 2/n = 322/323

2/1x3 + 2/3x5 + 3/5x7 + ... + 2/nx(n+2)  = 322/323 

1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + .... + 1/n-1 - 1/(n+2) = 322/323

1 - 1/n+2 = 322/323

1/n+2 = 1 - 322/323

1/n+2 = 1/323

=> x + 2 = 323

n = 323 - 2 = 321 

Answer 2

2/3 + 2/15 + 2/35 + ... + 2/n = 322/323

2/1x3 + 2/3x5 + 3/5x7 + ... + 2/nx(n+2)  = 322/323 

1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + .... + 1/n-1 - 1/(n+2) = 322/323

1 - 1/n+2 = 322/323

1/n+2 = 1 - 322/323

1/n+2 = 1/323

=> x + 2 = 323

n = 323 - 2 = 321