Recent questions tagged sequences-and-series

Let $a_{0}=0$ and define $a_{n}=\frac{1}{2}\left(1+a_{n-1}\right)$ for all positive integers $n \geq 1$. The least value of $n$ for which $\left|1-a_{n}\right|<\frac{1}{2...

Which one of the following is used for global alignment of two protein sequences?Chou-Fasman methodGarnier-Osguthorpe-Robson (GOR) methodNeedleman-Wunsch algorithmSmith-W...

The sum of the infinite geometric series $1 + 1/3 + 1/3^2+ 1/3^3+ \dots$ (rounded off to one decimal place) is ___________

An infinite series $S$ is given as:$S=1+2/3+3/9+4/27+5/81+\:.\dots$ (to infinity)The value of $S$ is ______________________ (round off to $2$ decimal places).

Which of the following are geometric series?$1,\:6,\:11,\:16,\:21,\:26,\:\dots$$9,\:6,\:3,\:0,\:-3,\:-6,\:\dots$$1,\:3,\:9,\:27,\:81,\:\dots$$4,\:-8,\:16,\:-32,\:64,\:\do...

Consider the following infinite series:$$1+ r+r^2 +r^3+ \dots \dots \infty$$ If $r = 0.3$, then the sum of this infinite series is ____________

If $1+r + r^2+ r^3 +\dots \infty = 1.5$, then, $1 + 2r + 3r^2 + 4r^3 + \dots \infty = $ (up to two dcimal places) ________