A series whose $n^{th}$ term is $\left( {\frac{n}{x}} \right) + y,$ the sum of $r$ terms will be
$\left\{ {\frac{{r(r + 1)}}{{2x}}} \right\} + ry$
$\left\{ {\frac{{r(r - 1)}}{{2x}}} \right\}$
$\left\{ {\frac{{r(r - 1)}}{{2x}}} \right\} - ry$
$\left\{ {\frac{{r(r + 1)}}{{2y}}} \right\} - rx$
Let the sequence $a_{n}$ be defined as follows:
${a_1} = 1,{a_n} = {a_{n - 1}} + 2$ for $n\, \ge \,2$
Find first five terms and write corresponding series.
The solution of ${\log _{\sqrt 3 }}x + {\log _{\sqrt[4]{3}}}x + {\log _{\sqrt[6]{3}}}x + ......... + {\log _{\sqrt[{16}]{3}}}x = 36$ is
If the ${p^{th}}$ term of an $A.P.$ be $\frac{1}{q}$ and ${q^{th}}$ term be $\frac{1}{p}$, then the sum of its $p{q^{th}}$ terms will be
If $\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}$ be the $A.M.$ of $a$ and $b$, then $n=$
If ${S_n}$ denotes the sum of $n$ terms of an arithmetic progression, then the value of $({S_{2n}} - {S_n})$ is equal to