A series whose $n^{th}$ term is $\left( {\frac{n}{x}} \right) + y,$ the sum of $r$ terms will be

  • A

    $\left\{ {\frac{{r(r + 1)}}{{2x}}} \right\} + ry$

  • B

    $\left\{ {\frac{{r(r - 1)}}{{2x}}} \right\}$

  • C

    $\left\{ {\frac{{r(r - 1)}}{{2x}}} \right\} - ry$

  • D

    $\left\{ {\frac{{r(r + 1)}}{{2y}}} \right\} - rx$

Similar Questions

The four arithmetic means between $3$ and $23$ are

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=n(n+2)$

Let ${\left( {1 - 2x + 3{x^2}} \right)^{10x}}  = {a_0} + {a_1}x + {a_2}{x^2} + .....+{a_n}{x^n},{a_n} \ne 0$, then the arithmetic mean of $a_0,a_1,a_2,...a_n$ is

If ${S_k}$ denotes the sum of first $k$ terms of an arithmetic progression whose first term and common difference are $a$ and $d$ respectively, then ${S_{kn}}/{S_n}$ be independent of $n$ if

The number of terms in an $A .P.$ is even ; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10\frac{1}{2}$ , then the number of terms in the $A.P.$ is

  • [JEE MAIN 2014]