Write the first five terms of each of the sequences and obtain the corresponding series:

$$a_1 = -1,a_n=\dfrac{a_{n-1}}{n},n ≥ 2$$

Asked by Abhisek | 1 year ago |  105

##### Solution :-

$$a_n=\dfrac{a_{n-1}}{n}$$ and a1 = -1

Then,

a2 = $$\dfrac{a_1}{2}$$ = $$- \dfrac{1}{2}$$

a3 = $$\dfrac{a_2}{3}$$ = $$- \dfrac{1}{6}$$

a4 = $$\dfrac{a_3}{4}$$ = $$- \dfrac{1}{24}$$

a5 = $$\dfrac{a_4}{5}$$ = $$- \dfrac{1}{120}$$

Thus, the first 5 terms of the sequence are -1, $$- \dfrac{1}{2}$$, $$- \dfrac{1}{6}$$$$- \dfrac{1}{24}$$ and $$- \dfrac{1}{120}$$.

Hence, the corresponding series is

-1 + ($$- \dfrac{1}{2}$$) + ($$- \dfrac{1}{6}$$) + ($$- \dfrac{1}{24}$$) + ($$- \dfrac{1}{120}$$) + …….

Answered by Pragya Singh | 1 year ago

### Related Questions

#### Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

#### Find the two numbers whose A.M. is 25 and GM is 20.

Find the two numbers whose A.M. is 25 and GM is 20.

#### If a is the G.M. of 2 and 1/4 find a.

If a is the G.M. of 2 and $$\dfrac{1}{4}$$ find a.

#### Find the geometric means of the following pairs of numbers

Find the geometric means of the following pairs of numbers:

(i) 2 and 8

(ii) a3b and ab3

(iii) –8 and –2

Insert 5 geometric means between $$\dfrac{32}{9}$$ and $$\dfrac{81}{2}$$.