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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesSpecial sequences/seriesMedium2 minQB

MathematicsMediummultiple choice

A few identical balls are arranged in a form whose base is an equilateral triangle and one side of the base triangle contains $n$ balls. Then

Options:(select one or more)

Answer:

B, C

Solution:

The base triangle has $1 + 2 + \dots + n = \frac{n ( n + 1 )}{2} = \frac{1}{2} (n^{2} + n)$ balls. The layers above have $\frac{k ( k + 1 )}{2}$ balls for $k =$ $n, n - 1, \dots, 1$ , so the pyramid has $\frac{1}{2} (\sum k^{2} + \sum k) = \frac{n ( n + 1 ) ( n + 2 )}{6}$ balls.

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Special sequences/series

⏱ 2mℹ️ Source: QB

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