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

If S_n denotes the sum of n terms of an AP whose common difference is d, the value of S_n - 2S_n-1 + S_n-2 is

The sum up to n terms of the series \(\frac { 1 }{ \sqrt { 1 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 3 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 7 } } +\)....is 

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

The sum up to n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +\).....is

The value of the series\(\frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 16 } +\).....is

The sum of an infinite GP is 18. If the first term is 6, the common ratio is

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

If \(\frac { { T }_{ 2 } }{ { T }_{ 3 } } \)is the expansion of (a+b)ⁿ and \(\frac { { T }_{ 3 } }{ { T }_{ 4 } } \) is the expansion of (a+b)ⁿ⁺³ are equal, then n = ______________

The Co-efficient of x^-17 in \({ \left( { x }^{ 4 }-\frac { 1 }{ { x }^{ 3 } } \right) }^{ 15 }\)is _____________ 

Find the sum of first n terms of the series 1² + 3² + 5²+...

Find a negative value of m if the Co-efficient of x² in the expansion of (1+x)m, |x|<1 is 6

Find the general term in the expansion of \({ \left( \frac { 4x }{ 5 } -\frac { 5 }{ 2x } \right) }^{ 9 }\)

Find the middle term in \({ \left( x-\frac { 1 }{ 2y } \right) }^{ 10 }\)

Find the greatest term in (1 + 2x)⁸ when x = 2.

Find the \(\sqrt [ 3 ]{ 126 } \) approximately to two decimal places.

If the roots of the equation (q - r) x² + (r - p)x + p - q = 0 are equal, then show that p, q and r are in A.P.

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of them \(\frac { (-1)^{ n } }{ n } \)

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

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of them 2018

Write the n^th term of the following sequences
\(\frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } \)

Expand \({\left( 2x-{1\over 2x} \right)}^{4}.\)

In a race, 20 balls are placed in a line at intervals of 4 meters, with the first ball 24 meters away from the starting point. A contestant is required to bring the balls back to the starting place one at a time. How far would the contestant run to bring back all balls?

Prove that \(\sqrt [ 3 ]{ x^3+7 } -\sqrt [ 3 ]{ x^3+4 } \) is approximately equal to \({1\over x^2}\) when x is large.