Show that `(5)/(6.12) + (5.8)/(6.12.18) + (5.8.11)/(6.12.18.24) + ….. = (3root(3)(4) -4)/(6)`

Show that (4)/(12.18) - (4.7)/(12.18.24) + (4.7.10)/(12.18.24.30) - …..= 3 root(3) (9/4) - 47/12

Sho that 3/6 + (3.5)/(6.9) + (3.5.7)/(6.9.12)+ ……..oo 3 sqrt3 - 4

(3)/(4.8)+(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)+….=

(4)/(1.3)-(6)/(2.4)+(12)/(5.7)-(14)/(6.8)+….=

Which is greater: (5)/(6) of (3)/(4) or (3)/(12) of (11)/(9) ?

Express as like fractions: (5)/(18), (7)/(12), (5)/(6)

If x = (1.3)/(3.6) + (1.3.5)/(3.6.9) + (1.3.5.7)/(3.6.9.12) + ….. then prove that 9x^2 + 24x = 11

Write four more rational numbers in each of the following patterns : (i) (-3)/5 , (-6)/10 , (-9)/15 , (-12)/20,..... (ii) (-1)/4 , (-2)/8, (-3)/12,...... (iii) (-1)/6, 2/(-12), 3/(-18), 4/(-24),....... (iv) (-2)/3 , 2/(-3) , 4/(-6), 6/-9,.......

Simplify : (i) (-2)/3+5/9-(-7)/6 (ii) 5/(12)+(-5)/(18)-7/(24)

Simplify : (i) (-2)/3+5/9-(-7)/6 (ii) 5/(12)+(-5)/(18)-7/(24)