Question 5 - A-Level Maths

Show that \(\sum _ { \mathrm { r } = 1 } ^ { \mathrm { n } } ( 2 \mathrm { r } - 1 ) = \mathrm { n } ^ { 2 }\).
Show that \(\frac { \sum _ { \mathrm { r } = 1 } ^ { \mathrm { n } } ( 2 \mathrm { r } - 1 ) } { \sum _ { \mathrm { r } = \mathrm { n } + 1 } ^ { 2 \mathrm { n } } ( 2 \mathrm { r } - 1 ) } = \mathrm { k }\), where \(k\) is a constant to be determined.