1 Express \(\frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }\) in partial fractions and hence use the method of differences to find
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }$$
Deduce the value of
$$\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }$$
Show LaTeX source
1 Express $\frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }$ in partial fractions and hence use the method of differences to find
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }$$
Deduce the value of
$$\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }$$
\hfill \mbox{\textit{CAIE FP1 2011 Q1}}