which one is the sum of the series $1\mathrm{ }–\mathrm{ }3\mathrm{ }+\mathrm{ }5\mathrm{ }–\mathrm{ }7\mathrm{ }+\mathrm{ }9\mathrm{ }–\mathrm{ }11\mathrm{ }+\dots$ upto n terms. .

$\text{ Let }{S}_n=1·(n-1)+2·(n-2)+3·(n-3)+\dots +(n-1)·1, n⩾4.$ 

$\text{The sum }\sum _{\mathrm{n}=4}^{\infty }\left(\frac{2{ \mathrm{S}}_{\mathrm{n}}}{\mathrm{n}!}-\frac{1}{(\mathrm{n}-2)!}\right)\text{ is equal to :}$ 

Consider the numbers between $100$ and $300$ which leaves remainder $2$ on division by $3$.

Which is the first number in this sequence?

Consider the numbers between $100$ and $300$ which leaves remainder $2$ on division by $3$.

Which is the last number in this sequence?