If $y = x - x^2 + x^3 - x^4 + \dots \infty$,then the value of $x$ will be

Given a sequence of $4$ numbers,the first three of which are in $G.P.$ and the last three are in $A.P.$ with a common difference of $6$. If the first and last terms in this sequence are equal,then the last term is:

The sum of the series $\frac{3}{1! + 2! + 3!} + \frac{4}{2! + 3! + 4!} + \frac{5}{3! + 4! + 5!} + \dots + \frac{2008}{2006! + 2007! + 2008!}$ is equal to

$A$ body falls $16\, m$ in the first second of its motion,$48\, m$ in the second,$80\, m$ in the third,$112\, m$ in the fourth and so on. How far does it fall during the $11^{th}$ second of its motion? (in $m$)

Find the sum of $1+\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\cdots$ to infinite terms.

After inserting $n$ arithmetic means $(A.M.s)$ between $2$ and $38$,the sum of the resulting progression is $200$. The value of $n$ is