$2.\overline{357} = $

For a series $S = 1 - 2 + 3 - 4 + \dots$ up to $n$ terms,
Statement-$1$: The sum of the series is always dependent on the value of $n$,i.e.,whether it is even or odd.
Statement-$2$: The sum of the series is $-\frac{n}{2}$ when the value of $n$ is any even integer.

If the $n^{th}$ term of a sequence is $T_n = 2n - 1$,then the sum of $n$ terms $S_n = \dots$

The mean of $10$ numbers $7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \ldots$ is ....... .

$2.5 + 5.9 + 8.13 + 11.17 + \ldots$ to $10$ terms $=$

$\sum_{k=1}^{\infty} \sum_{r=0}^k \frac{1}{3^k} \binom{k}{r}$ is equal to