Question

consider tbe sequence of numbers [n+√2n +1/2] for n>1 where [x] denotes the greatest integer not exceeding x. if the missing integers in the sequence are n1>n2>n3>....……. then find n12​

Answer 1

$\large\textbf{\underline{\underline{Question}}}\\\\\begin{minipage}{11.4cm}\normalsize Consider the sequence of numbers [n+\sqrt{2n}+\frac{1}{2}] for n\geq1, where [x] denotes the greatest integer not exceeding x . If the missing integers in the sequence are n_1<n_2<n_3<\cdots then find n_{12}. \end{minipage}$

$\large\textbf{\underline{\underline{Solution:}}}\\\\\begin{minipage}{11.4cm}\normalsize On taking values for n , the values of [n+\sqrt{2n}+\frac{1}{2}] follow the sequence:\\\\ 2,\ 4,\ 5,\ 7,\ 8,\ 9,\ 11,\dots \\\\This gives that the missing numbers are \textbf{triangular numbers}.\\\\ n_k=\frac{k(k+1)}{2} \\\\ Hence \ n_{12}=\frac{12\times 13}{2}=\mathbf{78.} \end{minipage}$

Answer 2

Answer:

my goodness only 25 points for this

Step-by-step explanation:

i won't answer you i need more marks