Expand \(\left( { 2x }^{ 2 }-\frac { 3 }{ x } \right) ^{ 3 }\)

Find the general terms and sum to n terms of the sequence 1, \(\frac{4}{3},\frac{7}{9},\frac{10}{27},....\)

A man repays an amount of Rs. 3250 by paying Rs. 20 in the first month and then increases the payment by Rs.15 per month. How long will it take him to clear the amount?

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?

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid.
\({ \left( x+2 \right) }^{ -\frac { 2 }{ 3 } }\)

Write the first 6 terms of the exponential series e^5x

Write the first 6 terms of the exponential series e^-2x

Write the first 6 terms of the exponential series \({ e }^{ \frac { 1 }{ 2 } x }\)

 If n is a positive integer and R is a nonnegative integer. prove that the co-efficients of x^r and x^n-r Expansion of (1+x)ⁿ are equal

Write the first 4 terms of the logarithmic series of \(\log { \left( \frac { 1+3x }{ 1-3x } \right) } \). Find the intervals on which the expansions are valid