Advertisements
Advertisements
Question
Find the sum of the following.
`(1 - 1/n) +(1 -2/n) + (1- 3/n) +` ......up to n terms.
Solution
On simplifying the given series, we get:
`(1 - 1/n) +(1 -2/n) + (1- 3/n) +` .... n terms
`=(1+1+1+ .......... "n terms") - (1/n+2/n+3/n+ .......+n/n)`
`= n - ( 1/n + 2/n +3/n + ..................+ n/n)`
` Here, (1/n +2/n +3/n +........+n/n) " is an AP whose first term is" 1/2 "and the common difference"`
is `(2/n - 1/n) = 1/n.`
The sum of terms of an AP is given by
`s_n = n/2 [ 2a + (n-1) d ] `
`= n - [ n/2{ 2 xx (1/n) + (n-1) xx (1/n) }]`
` = n -[ n/2 [ (2/n) + ((n-1)/n) ]] = n- { n/2((n+1)/n) }`
`=n- ((n+1)/2) = (n-1)/2`
APPEARS IN
RELATED QUESTIONS
In an AP, the first term is 22, nth terms is -11 and sum of first n terms is 66. Find the n and hence find the4 common difference.
Two Aps have the same common difference. If the fist terms of these Aps be 3 and 8 respectively. Find the difference between the sums of their first 50 terms.
The sum of the 4th and 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find the sum of its first 10 terms.
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees that each section of each class will plant will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two section, find how many trees were planted by student. Which value is shown in the question?
Sum of first 55 terms in an A.P. is 3300, find its 28th term.
The estimated tax on the income of Shreemati Hinduja is Rs. 8000. How much education cess has she to pay at 3% ?
A = {1, 2, 3,4, 5}, B = {5, 6, 7} write AUB .
Write the lower and the uppper class limit of 35 to 40
Find the eighteenth term of the A.P: 1, 7, 13, 19, ............
If for an A.P. the first term is 2 and the common difference is 3, then find first three-term of A.P.
