Question

[Văn Hoàng Nguyên]

Cho A = 1/2 + 1/6 + 1/12 + 1/20 +1/30 + ....... + 1/n . Biết A = 49/50 . Tìm n .

1560

2450

Answer 1

[Đinh Đức Hùng]

<=> A = 1/1.2 + 1/2.3 + 1/3.4 + ..... + 1/a.( a + 1 ) = 49/50 [ a.( a + 1 ) = n ]

<=> A = 1/1 - 1/2 + 1/2 - 1/3 + ....... + 1/a - 1/a + 1 = 49/50

<=> A = 1 - 1/a + 1 = 49/50

<=> A = 1/a + 1 = 1 - 49/50

<=> A = 1/a + 1 = 1/50

=> a + 1 = 50

=> n = 50. ( 50 - 1 ) = 2450

Vậy n = 2450

Answer 2

[Viên Kẹo Ước Ngọt Ngào]

1/2 = 1/(1x2) = 1 - 1/2

1/6 = 1/(2x3) = 1/2 - 1/3

1/12 = 1/(3x4) = 1/3 - 1/4

........

1/n = 1/(ax(a+1)) = 1/a - 1/(a+1)

1 /2 + 1/6 + 1/12 + 1/20 + 1/30 +...+ 1/n = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+1/a - 1/(a+1) = 49/50

Hay A = 1 - 1/(a+1) = 49/50

=> 1/(a+1) = 1 - 49/50

      1/(a+1) = 1/50

Vậy (a + 1) = 50 mà n = a x (a+1) => n = (50-1) x 50 = 2450