# Science:Math Exam Resources/Courses/MATH220/April 2011/Question 07 (a)

MATH220 April 2011
Other MATH220 Exams

### Question 07 (a)

Let ${\displaystyle \{a_{n}\}}$ be a sequence of real numbers defined by

${\displaystyle a_{1}=1\quad {\text{ and }}\quad a_{n+1}=2a_{n}+1\quad {\text{ for each }}n\in \mathbb {N} .}$

Prove that

${\displaystyle a_{n}=2^{n}-1\quad {\text{ for all }}n\in \mathbb {N} .}$
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