Question

1/6+1/12+1/20+1/30+....+1/9900=?

Answer 1

Answer:

49/100

Step-by-step explanation:

=1/2(3)+1/3(4)+1/4(5)+1/5(6)+..........+1/99(100)

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+....+1/90-1/100

=1/2-1/100

=49/100

Answer 2

Answer:

Hey buddy..

Step-by-step explanation:

1/2 = 1 - 1/2

1/6 = 1/2-1/3

1/12 = 1/3 - 1/4

1/9900 = 1/x - [1/x+1]

1/9900 = 1/(x^2+x)

x^2 + x = 9900

x^2+x-9900 = 0

(x+100)(x-99) = 0

x=-100 or 99

x>0...........[Each nth term I'm the series, where n is odd(1st, 3rd, 5th and so on....) in the series is positive.]

Therefore 1/9900 = 1/99 - 1/100

1 - 1/2

+1/2 - 1/3

+1/3 - 1/4

+1/4 - 1/5

+1/5 - 1/6......

+1/98 - 1/99

As a result each term, with the exclusion of 1 and -(1/100) get cancelled by their negatives.

Therefore, our answer is 1 - 1/100 = 99/100 = 0.99.

Hope my answer seemed useful and appropriate to you......