Arithmetic Geometric Series
- A series will be an arithmetic-geometric series if each of its terms is formed by the product of the corresponding terms of an A.P and G.P.
- The general form of A.G.P series is a, (a+d)r, (a+2d)$$r^{2}$$,......
- Sum of ‘n’ terms of A.G.P series
$$S_{n}$$=$$\frac{a}{1-r}$$+rd$$\frac{(1-r^{n-1})}{1-r}$$+rn$$\frac{[a+(n-1)d]}{1-r}$$(r≠1)
- Sum of infinite terms of A.G.P series
$$S_{∞}$$=$$\frac{a}{1-r}+\frac{dr}{(1-r)^{2}}$$(|r|<1)
