Sum to n terms of $1^2+3^2+5^2+\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}1^2+3^2+5^2+.......$ is

The seventh term in the sequence $1,\frac{-1}{2},\frac{1}{4},\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}1\; ,\; \backslash frac\{-1\}\{2\},\; \backslash frac\{1\}\{4\},\; ..........$

Sum to ‘n’ terms of $2^3+4^3+6^3+\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}2^3+4^3+6^3+\; .......$ is

The common ratio of G.P. $1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}1-\; \backslash frac\{1\}\{3\}+\backslash frac\{1\}\{9\}-\backslash frac\{1\}\{27\}+........$ is

$1+(0.04)+(0.04{)}^2+\dots \dots \mathrm{.}\mathrm{\infty }=1\; +\; (0.04)\; +\; (0.04)^2\; +\; \dots \dots .\; \backslash infty\; =$

If $\mathrm{\mid }x\mathrm{\mid }|x|$ < $1,y=x-x^2+x^3-x^4+\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{\infty }1,y=x-x^2+x^3-x^4+.......\backslash infty$, then the value of x in terms of y is

Coefficient of $x^{2}x^2$ in (x + 1) (x + 2) (x + 3) (x + 4) (x + 5) is …………

If the sum of the three numbers in a G.P is 26 and the sum of products taken two at a time is 156, then the numbers are

If the sum of three numbers in G.P is $\frac{7}{64}\backslash frac\{7\}\{64\}$ and the product of the extremes is $\frac{1}{1024}\backslash frac\{1\}\{1024\}$ then the numbers are

If $p^{th},q^{th},r^{th}p^\{th\}\; ,q^\{th\}\; ,r^\{th\}$  terms of a G.P are a, b, c then Σ(q – r) log a =