Write first five terms of sequences whose n^{t h} term is a_{n}=frac{n}{n+1}

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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

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(JEE MAIN-2025)