OCR MEI Further Pure Core AS 2019 June — Question 1 3 marks

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2019
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSequences and series, recurrence and convergence
TypeMethod of differences with given identity
DifficultyStandard +0.3 This is a straightforward method of differences question where the telescoping form is already given. Students need only write out the first few and last few terms to identify what survives, then evaluate. While it requires careful bookkeeping and understanding of telescoping series, it's a standard technique with no conceptual obstacles or novel insight required.
Spec4.06b Method of differences: telescoping series

1 In this question you must show detailed reasoning.
Find \(\sum _ { r = 1 } ^ { 100 } \left( \frac { 1 } { r } - \frac { 1 } { r + 2 } \right)\), giving your answer correct to 4 decimal places.

Question 1:
AnswerMarks
1DR
1001 1  1 1 1 1 1 1 1
∑ − =1− + − + − +K + −
 
r r+2 3 2 4 3 5 100 102
r=1
1 1 1
=1+ − −
2 101 102
AnswerMarks
= 1.4803 (4 d.p.)M1
A1
A1cao
AnswerMarks
[3]2.5
2.2a
AnswerMarks
1.1must see at least one
cancellation
1 1 1
or 1+ − −
2 n+1 n+2
must be to 4 DP
Question 1:
1 | DR
1001 1  1 1 1 1 1 1 1
∑ − =1− + − + − +K + −
 
r r+2 3 2 4 3 5 100 102
r=1
1 1 1
=1+ − −
2 101 102
= 1.4803 (4 d.p.) | M1
A1
A1cao
[3] | 2.5
2.2a
1.1 | must see at least one
cancellation
1 1 1
or 1+ − −
2 n+1 n+2
must be to 4 DP
1 In this question you must show detailed reasoning.\\
Find $\sum _ { r = 1 } ^ { 100 } \left( \frac { 1 } { r } - \frac { 1 } { r + 2 } \right)$, giving your answer correct to 4 decimal places.

\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2019 Q1 [3]}}