Moderate -0.3 This is a straightforward telescoping series question where the identity is already given in the required form. Students simply need to write out the first few and last few terms to see the cancellation pattern, then evaluate what remains: 1 + 1/2 - 1/50 - 1/51. While it requires careful bookkeeping and fraction arithmetic, it's a standard textbook exercise with no conceptual difficulty or novel insight required, making it slightly easier than average.
1 In this question you must show detailed reasoning.
Find \(\sum _ { r = 2 } ^ { 50 } \left( \frac { 1 } { r - 1 } - \frac { 1 } { r + 1 } \right)\), expressing the answer as an exact fraction.
1 In this question you must show detailed reasoning.
Find $\sum _ { r = 2 } ^ { 50 } \left( \frac { 1 } { r - 1 } - \frac { 1 } { r + 1 } \right)$, expressing the answer as an exact fraction.
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2020 Q1 [3]}}