List of top Mathematics Questions on Sequences and Series asked in TS EAMCET

If \[ x=2+\frac{7}{8}+\frac{7\cdot10}{8\cdot12}+\frac{7\cdot10\cdot13}{8\cdot12\cdot16}+\cdots, \] then \(x^3=\)

If \(S(n):2n<n!\), \(n\in\mathbb N\), then \(S(n+1)\) is true for all \(n\ge\):

If \[ 1+3+5+\cdots+l_1=1521 \] and \[ 2+4+6+\cdots+l_2=1722, \] then $l_1+l_2=$

Consider the following Assertion and Reason Assertion: \[ \frac{1}{5\cdot9}+\frac{1}{9\cdot13}+\frac{1}{13\cdot17}+... \text{ to 10 terms }=\frac{9}{41} \] Reason: \[ \text{For all }n\in N, \quad \frac{1}{5\cdot9}+\frac{1}{9\cdot13}+... =\frac{n}{5(4n+5)} \]

If $2^{4n+3} + 3^{3n+1}$ is divisible by P for all natural numbers $n$, then P is

The value of the greatest integer k satisfying the inequation $2^{n+4} + 12 \geq k(n+4)$ for all $n \in N$ is

If $\frac{1}{2.7} + \frac{1}{7.12} + \frac{1}{12.17} + \dots$ to 10 terms = k, then k =