Sum of the following series to `n` term: `3+5+9+15\ +23+........`

Explanation

`3+5+9+15+23+ldots+T_{n-1}+T_{n}`


The difference between the successive terms are s difference are in A.p.


Let `S_{n}` denote the sum to n terms of the given series


Then,` S_{n}=3+5+9+15+23+cdots+T_{n-1}+T_{n} cdots(1)`


Also `S_{n}=3+5+9+15+ldots+T_{n}-1+ T_{n} cdots-(1)`


Also ` S_{n}=3+5+9+15 t ldots+T_{n}-1 + T_{n} ldots(2)`


subtracting (2) from (1) we get


`0=3+frac{(n-1)}{2}[2 times 2+(n-1-1) times 2)]`


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