List of top Mathematics Questions on Sequence and Series

Arithmetic mean of two numbers \(a\) and \(b\) is \(5\) and the harmonic mean is \(3.2\). Find the numbers \(a\) and \(b\)?

Consider the sequence: 72, 69, 66, ---. The numbers continue in the same pattern as long as they remain positive. What will be the maximum possible sum of the terms of this sequence?

72, 69, 66, \(\ldots\) Number continue in same pattern as long as they remain positive. What will be the maximum sum of terms?

Find the value of \(n\) if \[ \left(\sum_{k=1}^{n}(-1)^{k-1}k\right)^2 - \sum_{k=1}^{n}(-1)^{k-1}k^2 +2450=0. \]

Let \(A_k\) be the arithmetic mean of the squares of \(k\) natural numbers. \[ \sum_{k=1}^{n}(6A_k-3k)=31 \] Find the value of \(n\):

Find the value of $(1 - \frac{1}{2})(1 - \frac{1}{3})(1 - \frac{1}{4}) \dots (1 - \frac{1}{n})$.

The value of $\cot\left(\sum_{n=1}^{23}\cot^{-1}\left(1+\sum_{k=1}^{n}2k\right)\right)$ is

Evaluate (x+\frac1x)²+(x²+\frac1x²)²+(x³+\frac1x³)² up to n terms is

The sum to n terms of the series \frac12+\frac34+\frac78+(15)/(16)+⋯ is

If the mean of the first \(n\) odd numbers is \( \frac{n^2}{81} \), then \(n\) equals

The sum \[ 1 + \frac{1+a}{2!} + \frac{1+a+a^2}{3!} + \cdots \] is equal to:

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

If $a_1, a_2, a_3, a_4$ are in A.P., then $\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \frac{1}{\sqrt{a_3} + \sqrt{a_4}} =$

The sum of the series $\sum_{n=8}^{17} \frac{1}{(n+2)(n+3)}$ is equal to:

Let \( s_n = \cos\left(\frac{n\pi}{10}\right) \), \( n=1,2,3, \ldots \). Then the value of \( \frac{s_1s_2\cdots s_{10}}{s_1+s_2+\cdots+s_{10}} \) is equal to:

The sum of the series \( \sum_{n=8}^{17} \frac{1}{(n+2)(n+3) \) is equal to:}

Let \( s_n = \cos\left(\frac{n\pi}{10}\right) \), \( n=1,2,3, \ldots \). Then the value of \( \frac{s_1s_2\cdots s_{10}}{s_1+s_2+\cdots+s_{10}} \) is equal to: