A pattern of numbers is given below. Row 1: 1/(1×2) = 1/1 - 1/2 Row 2: 1/(2×3) = 1/2 - 1/3 Row 3: 1/(3×4) = 1/3 - 1/4 Row 4: 1/(4×5) = 1/4 - 1/5

1. (a)Write down Row 10.[1]
2. (b)(i)Adding the first two rows gives the result 1/(1×2) + 1/(2×3) = 1 - 1/3 = 2/3. Adding the first three rows gives the result 1/(1×2) + 1/(2×3) + 1/(3×4) = 1 - 1/4 = 3/4. Write down the result of adding the first four rows.[1]
3. (b)(ii)(α)Use the pattern to write down the value of 1/(1×2) + 1/(2×3) + 1/(3×4) + ... + 1/(19×20).[1]
4. (b)(ii)(β)the number of rows that add up to 109/110.[1]
5. (c)an expression, in terms of n, for the result of adding the first n rows.[1]