List of top Mathematics Questions on Series asked in BITSAT

The coefficient of \(x^n\) in the expansion of \[\frac{e^{7x} + e^x}{e^{3x}}\] is:

The sum of the infinite series \(1 + \frac{5}{6} + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} + \dots\) is equal to:

If \( A = 1 + r^a + r^{2a} + r^{3a} + \dots \infty \) and \( B = 1 + r^b + r^{2b} + r^{3b} + \dots \infty \), then \( \frac{a}{b} \) is equal.

There are four numbers of which the first three are in GP and the last three are in AP, whose common difference is 6. If the first and the last numbers are equal, then the two other numbers are:

If \( \sum_{k=1}^{n} k(k+1)(k-1) = pn^4 + qn^3 + tn^2 + sn \), where \( p, q, t, s \) are constants, then the value of \( s \) is equal to:

\( \left(x + \dfrac{1}{x}\right)^2 + \left(x^2 + \dfrac{1}{x^2}\right)^2 + \cdots + \left(x^n + \dfrac{1}{x^n}\right)^2 \)
upto \( n \) terms is

If \[ \frac{e^x+e^{5x}}{e^{3x}}=a_0+a_1x+a_2x^2+a_3x^3+\cdots, \] then the value of \(2a_1+2^3a_3+2^5a_5+\cdots\) is

The sum of the series \[ 1 + 2^2 + 3^2 + 4^2 + \dots + 100^2 \] is