Question

2/3 + 2/15 + 2/ 35+...+ 2/n=60/61 . Vay n=...

Answer 1

Nếu 2/3 + 2/15 + 2/35 + ................+2 /A = 60/61.Tìm A

Giải

Đặt B = 2/3 + 2/15 + 2/35 + ................+2 /A

= 2/(1x3) + 2/3x5 + 2/5x7 + ... + 2/a x (a+2) (trong đó A = a x (a +2)

= 3/1x3 - 1/1x3 + 5/3x5 - 3/3x5 +7/5x7 - 5/5x7 +... + (a+2)/a x (a + 2) - a/a x (a+2)

=1 - 1/3+1/3 -1/5+1/5 - ... - 1/(a + 2)

= 1 - 1/(a + 2)

Vậy 1 - 1/(a + 2) = 60/61

=> (a + 1)/ (a + 2) = 60/61

=> a = 59

Mà A = a x (a +2) nên A = 59 x (59 + 2) = 59 x 61 = 3599

ĐS: A = 3599