Sequences and S...

Let $$S_n=\dfrac{1}{1+2008n}+\dfrac{1}{2+2008n}+...+\dfrac{1}{2009n}$$. Then $$\displaystyle\lim_{n\rightarrow\infty}S_n$$ equals?

If $$\frac{a_2a_3}{a_1a_4}=\frac{a_2+a_3}{a_1+a_4}=3\left(\frac{a_2-a_3}{a_1-a_4}\right)$$ then $$a_1, a_2$$ and $$a_3$$ are in which progression?

The sum of all $$2$$-digit numbers divisible by $$5$$ is _________?

The $$15^{th}$$ terms of the series $$2\dfrac{1}{2} + 1\dfrac{7}{13} + 1\dfrac{1}{9} + \dfrac{20}{23} +$$_____ is

If $$S_r=\left |
\begin{array}{111}
2r & x & n(n+1)\\
6r^2-1 & y & n^2(2n+3)\\
4r^3-2nr & z & n^3(n+1)\\
\end{array}
\right |
$$ then $$\sum_\limits{r=1}^n S_r$$
does not depends on

Insert the missing number in the given series : $$ 0,4,18,48, ?, 180$$ 

Ten students of the physics department decided to go on a educational trip.They hired a mini bus for the trip, but the bus can only carry eight students at a time and each student goes at least once. Find the minimum number of trips the bus has to make so that each students can go for equal number of trips.

For a sequence $$\left\{ { a }_{ n } \right\} ,{ a }_{ 1 }=2$$ and $$\dfrac { { a }_{ n+1 } }{ { a }_{ n } } =\dfrac { 1 }{ 3 }$$. Then $$\sum _{ r=1 }^{ 20 }{ { a }_{ r } } $$ is

Number of rectangles in the grid shown which are not squares is?

$$1,2,1,4,3,8,9,5,27,16,?,?,?$$