The value of `sum_(r=1)^n{(2r-1)a+1/(b^r)}` is equal to (a)`a n^2+(b^(n-1)-1)/(b^n(b-1))` . (b) `a n^2+(b^(n)-1)/(b^n(b-1))` (c) `a n^3+(b^(n-1)-1)/(b^n(b-1))` (d) none of these

Explanation

Let `sum_(r=1)^n{(2r-1)a+1/(b^r)}`


`=>S=2asum_(r=1)^nr−asum_(r=1)^n1+sum_(r=1)^n(1/b^r​)`

using formula,
`S_n=(a(r^n-1))/(r-1)`
here,
`a=1/b` and `r=1/b`

So,


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