Question 12 Write the first five terms of the following sequence and obtain the corresponding series: a1 = -1, an = a(n-1)/n, n ≥ 2
Class X1 - Maths -Sequences and Series Page 181
Answers
hence, first five terms are -1/2 , -1/6 , -1/24 , -1/120, -1/720
Given:
a1 = - 1
an = a(n-1)/n, n ≥ 2
To Find:
The First five terms of the following sequence and obtain the corresponding series.
Calculating:
When we put the value of n as 2:
a2 = a2 - 1 / 2
= a1 / 2
= - 1 / 2 (Putting Value of a1 = - 1)
When we put the value of n as 3:
a3 = a3 - 1 / 3
= a2 / 3
= - 1/2 / 3 (Putting Value of a2 = -1/2)
Rearranging to multiply:
= (- 1/2) (1/3)
= - 1/6
When we put the value of n as 4:
a4 = a4-1 / 4
= a3 / 4
= -1/6 / 4 (Putting the value of a3 = -1/6)
Rearranging to multiply:
= (-1/6)(1/4)
= -1/24
When we put the value of n as 5:
a5 = a5-1 / 5
= a4 / 5
= -1/24 / 5 (Putting the value of a4 -1/24)
Rearranging to multiply:
= (- 1/24) (1/5)
= -1/120
Therefore, the first five terms of this sequence is -1, -1/2, -1/6, -1/24,-1/20.
Obtaining the corresponding series (-1)+ (-1/2) + (-1/6) + (-1/24) + (-1/120)+.......