Recent questions tagged sequences-and-series

Match each entry of $\text{List-1}$ with a suitable entry in $\text{List-2}$ and choose the correct option.$\textbf{List-1}$$\textbf{List-2}$$\mathrm{P}$$\text{The sum of...

Consider a five-digit number $PQRST$ that has distinct digits $P,Q,R,S$, and $T$, and satisfies the following conditions:$$\begin{array}{c} P<Q \\ S>P>T \\ R<T \end{array...

​Consider the infinite series$$ \begin{array}{l} \text { (P) }: \sum_{n=2}^{\infty} \frac{1}{(n \log n)^{1 / n}} \\\text { (Q): } \sum_{n=1}^{\infty} \frac{n^{n}}{(2 n)!}...

​​​​Suppose the polynomial $a+b x+c x^{2}+d x^{3}$ interpolates the data, $(-1,1),(0,3),(1,2)$ and $(2,4)$.Then which one of the following statements is correct?$a=-2 c, ...

Let\[f(x)=\left\{\begin{array}{cr}\pi+x, & -\pi \leq x<0, \\0, & 0 \leq x<\pi,\end{array}\right.\]with $f(x+2 \pi)=f(x)$. If $F(x)$ represents the Fourier series of $f(x)...

In the sequence $6,9,14, x, 30,41$, a possible value of $x$ is$25$$21$$18$$20$

A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ ...

Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:1. At any stage, Ankita can move either one or two stairs up.2. At any stage, An...