The numerical pattern below is given: Row 1 $\frac{1}{1\times2}=\frac12$, Row 2 $\frac{1}{2\times3}=\frac12-\frac13$, Row 3 $\frac{1}{3\times4}=\frac13-\frac14$, Row 4 $\frac{1}{4\times5}=\frac14-\frac15$.
(b(i))[1]
State the value obtained by adding the first four rows.
(b(ii)(a))[1]
Use the pattern to state the value of $\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\cdots+\frac{1}{19\times20}$.
(b(ii)(b))[1]
Use the pattern to state how many rows add to $\frac{109}{110}$.
(b(ii)(c))[1]
Use the pattern to write an expression, in terms of $n$, for the sum of the first $n$ rows.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\frac1{10\times11}=\frac1{10}-\frac1{11}$” …
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