If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

The HM of two positive numbers whose AM and GM are 16, 8 respectively is

The n^th term of the sequence \(\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 } \),......is

The coefficient of x⁵ in the series e^-2x is

The value of 2 + 4 + 6 + + 2n is

Compute 9⁷

Write the first 6 terms of the sequences whose n^th term a_n given below
\({ a }_{ n }=\begin{cases} n+1\quad if\quad n\quad is\quad odd \\ n\quad \quad if\quad n\quad is\quad even \end{cases}\)

Find the middle terms in the expansion of (x + y)⁷.

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid.
\(\frac { 1 }{ 5+x } \)

Write the first 6 terms of the sequences whose n^th terms are given below and classify them as arithmetic progression, geometric progression, arithmetic geometric progression, harmonic progression and none of them \(\frac { \left( n+1 \right) \left( n+2 \right) }{ \left( n+3 \right) (n+4) } \)

Expand \({1\over(1+3x)^2} \) in powers of x. Find a condition on x for which the expansion is valid.

Find the value of n if the sum to n terms of the series \(\sqrt { 3 } +\sqrt { 75 } +\sqrt { 243 } +....is\quad 435\sqrt { 3 } .\)

Find the sum of the first 20-terms of the arithmetic progression having the sum of first 10 terms as 52 and the sum of the first 15 terms as 77.