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find the sum of n terms of the series (4...

find the sum of `n` terms of the series `(4-1/n)+(4-2/n)+(4-3/n)+...........`

Text Solution

Verified by Experts

We are given the series
`S=(4-(1)/(n))+(4-(2)/(n))+(4-(3)/(n))+...` to n terms
`(4+4+4+..... "to n terms" )-((1)/(n)+(2)/(n)+(3)/(n)+... "to n terms")`
`4n-(1)/(n)(1+2+3+...."to n terms")`
`=4n(1)/(n)[(n)/(2){2xx1+(n-1)xx1}] " " `(`:' a=1, d=1`)
`=4n-(1)/(n)[(n)/(2)(n+1)]=4n-(n+1)/(2)=(8n-n-1)/(2)=(1)/(2)(7n-1)`
Hence, the required sum of n terms is `(1)/(2)(7n-1)`.
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