(1+2/3) / (2+1/2)?

(1 + 2/3) / (2 + 1/2)

=(5/3) / (5/2)

Dividing 2 fractions is like multiplying the numerator by the reciprocal of the denominator:

=(5/3) * (2/5)

=10/15

=2/3

(1+2/3) / (2+1/2)=[(3+2)/2]/[(4+1)/2]

=5/3*2/5=2/3

(1+2/3) / (2+1/2)

( 3/3 + 2/3 ) / ( 4/2 + 1/2 )

( 5/3 ) / ( 5/2 )

( 5*2 ) / ( 5*3 )

( 10 ) / ( 15 )

10 / 15 = 2 / 3 (same result)

Can not be simplified any more

Get common denominators so you can add the fractions (add the top together, add the bottom together)

1=3/3, 2=4/2

(3/3 + 2/3)/(4/2 + 1/2)

(5/3)/(5/2)

When you divide by a fraction, multiply by the reciprocal:

(5/3) x (2/5)= 2/3

(1 + 2/3)/(2 + 1/2)

= (5/3)/(5/2)

= 5/3 x 2/5

= 10/15 (divided numerator and denominator by 5)

= 2/3

I understand that you are asking sum as n -> ∞ nth term = 1 / Σn = 2 / [n(n + 1)] Required sum = 2 Σ 1 / [n(n + 1)] ( n=1 to ∞ ) = 2 Σ [ 1/n - 1/(n +1) ] ( n=1 to ∞ ) = 2 [ 1 - 1/(n + 1) ] ( n=1 to ∞ ) = 2.