Find \(\sqrt [ 3 ]{ 1001 } \) approximately. (two decimal places).

Prove that \(\sqrt [ 3 ]{ { x }^{ 3 }+6 } -\sqrt [ 3 ]{ { x }^{ 3 }+3 } \) is approximately equal to \(\frac { 1 }{ { x }^{ 2 } } \) when x is sufficiently large.

The first term of a G.P is 1. The sum of third and fifth terms is 90. Find the common ration of the G.P

Find all the sequence which are simultaneously arithmetic and geometric progression.

If the m^th term of a H.P is n and n^th term is m, then show that its p^th  term is \(\frac{mn}{p}\).

Find the sum : \(1+{4\over5}+{7\over 25}+{10\over125}+.....\)

Find the coefficient of the term involving x³² and x^-17 in the expansion of \((x^{4}-\frac{1}{x^{3}})^{15}\).

If the sum of the coefficients in the expansion of (x+y)ⁿ is 4096. Then find the greatest coefficient in the expansion.

If the ratio of the sums of m terms and n terms of an A.P. be m² : n², prove that the ratio of its mth and nth terms is (2m - 1) : (2n - 1).

The sum of first three terms of a G.P. is to the sum of the first six terms as 125: 152. Find the common ratio of the G.P.