Look at the denominators :

1st line : 6 = 3 × 2
2nd line : 12 = 4 × 3
3rd line : 20 = 5 × 4
4th line : 30 = 6 × 5

You can see that the numbers on the right hand side of the equation keep increasing by 1.

And so on. So for p,

p = 12 × 11 = 132 (answer for (b))

For the 5th line, the denominator on the left hand side will be : 7 × 6 = 42

So the 5th line is : 1/42 + 1/7 = 1/6 (answer for (a))


For (c) , let 1/n = 1/98 - 1/99

Then, 1/n + 1/99 = 1/98

Recall the pattern from above. n is just equal to 99 × 98 = 9702

Or,

1/n = 1/98 - 1/99 = 1/(99×98) = 1/9702

By the way, based on the pattern above, the general equation for the nth line would be :


1/(n+1)(n+2) + 1/(n+2) = 1/(n+1)