4 - 1/n + 4 - 2/n + 4 - 3/n +.....upto n terms: find the sum

Solution:

Given, the series is 4 - 1/n + 4 - 2/n + 4 - 3/n +.....upto n terms.

We have to find the sum of the series upto n terms.

The given series can also be written as

4n - (1/n + 2/n, ………….+ n/n)

= 4n - (1+2+3+.....+n)/n

The sum of the first n natural numbers is given by

S = n(n+1)/2

So, the series can be rewritten as

= 4n - n(n+1)/2n

Cancelling out common term,

= 4n - (n+1)/2

= 8n - n - 1/2

= (7n - 1)/2

Therefore, the sum of the term is (7n-1)/2.

✦ Try This: Find the sum: 3 + 1/n + 3 + 2/n + 3 + 3/n +.....upto n terms

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 21 (ii)

4 - 1/n + 4 - 2/n + 4 - 3/n +.....upto n terms: find the sum

Summary:

The sum of the terms 4 - 1/n + 4 - 2/n + 4 - 3/n +.....upto n terms is (7n-1)/2.

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