Question 6 - A-Level Maths

6 Prove by induction that \(\sum _ { r = 1 } ^ { n } r 2 ^ { r - 1 } = 1 + ( n - 1 ) 2 ^ { n }\).

6 Prove by induction that $\sum _ { r = 1 } ^ { n } r 2 ^ { r - 1 } = 1 + ( n - 1 ) 2 ^ { n }$.

\hfill \mbox{\textit{OCR MEI FP1  Q6}}