- Home
- Standard 11
- Mathematics
8. Sequences and Series
easy
Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=\frac{n}{n+1}$
A
$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}$
B
$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}$
C
$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}$
D
$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}$
Solution
$a_{n}=\frac{n}{n+1}$
Substituting $n=1,2,3,4,5,$ we obtain
${a_1} = \frac{1}{{1 + 1}} = \frac{1}{2},$
${a_2} = \frac{2}{{2 + 1}} = \frac{2}{3},$
${a_3} = \frac{3}{{3 + 1}} = \frac{3}{4},$
${a_4} = \frac{4}{{4 + 1}} = \frac{4}{5},$
${a_5} = \frac{5}{{5 + 1}} = \frac{5}{6}$
Therefore, the required terms are $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}$ and $\frac{5}{6}$
Standard 11
Mathematics
