List of top Mathematics Questions on Sequence and series asked in AP EAPCET

Find the sum of the infinite series \[ -1+\frac{7}{10}\cdot 2^2-\frac{7\cdot 9}{10\cdot 15}\cdot 2^3+\frac{7\cdot 9\cdot 11}{10\cdot 15\cdot 20}\cdot 2^4-\cdots\infty \]

Assertion (A): If \[ 2+6+16+40+\cdots \text{ to } k \text{ terms}=4608, \] then \(k=9\). Reason (R): \[ 2+3\cdot2+4\cdot2^2+\cdots+n\cdot2^{\,n-1}=n\cdot2^n, \qquad \forall n\in\mathbb N \] Which one of the following options is correct?

If \[ a_n= \sqrt{7+\sqrt{7+\sqrt{7+\cdots}}} \] (\(n\) radicals), then which of the following is true?