Easy -1.8 This is a 1-mark multiple choice question requiring only recall of the convergence condition for geometric series (|r| < 1). Students simply identify which series has common ratio with absolute value less than 1 (the third option with r = -1/2), making it significantly easier than average A-level questions.
Each of the series below shows the first four terms of a geometric series.
Identify the only one of these geometric series that is convergent.
[1 mark]
Tick (\(\checkmark\)) one box.
\(0.1 + 0.2 + 0.4 + 0.8 + \ldots\)
\(1 - 1 + 1 - 1 + \ldots\)
\(128 - 64 + 32 - 16 + \ldots\)
\(1 + 2 + 4 + 8 + \ldots\)
Each of the series below shows the first four terms of a geometric series.
Identify the only one of these geometric series that is convergent.
[1 mark]
Tick ($\checkmark$) one box.
$0.1 + 0.2 + 0.4 + 0.8 + \ldots$
$1 - 1 + 1 - 1 + \ldots$
$128 - 64 + 32 - 16 + \ldots$
$1 + 2 + 4 + 8 + \ldots$
\hfill \mbox{\textit{AQA Paper 3 2024 Q1 [1]}}