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Find the sum of the series $2 + 4 + 7 + 11 + 16 + \dots$ up to $n$ terms.

Let $a_{n}$ be the $n^{\text{th}}$ term of the series $5+8+14+23+35+50+\ldots$ and $S_{n}=\sum_{k=1}^{n} a_{k}$. Then $S_{30}-a_{40}$ is equal to

The product $(32)(32)^{1/6}(32)^{1/36} \dots \infty$ is

Find the sum of the series $1 + (1 + 2) + (1 + 2 + 3) + \dots$ up to $n$ terms.

If $[x]$ denotes the greatest integer less than or equal to $x$,then $\sum_{n=8}^{100} \left[ \frac{(-1)^{n} n}{2} \right]$ is equal to:

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