A) \[0\]
B) \[n\]
C) \[na\]
D) \[nar\]
Correct Answer: B
Solution :
\[{{S}_{n}}=\frac{a({{r}^{n}}-1)}{r-1}\] \[\Rightarrow \] \[{{U}_{n}}=\sum\limits_{n=1}^{n}{{}}\frac{a({{r}^{n}}-1)}{r-1}=\frac{a}{r-1}\sum\limits_{n=1}^{n}{({{r}^{n}}-1)}\] \[\Rightarrow \] \[{{U}_{n}}=\frac{a}{x-1}\{r+{{r}^{2}}+...+{{r}^{n}}-n\}\] \[=\frac{a}{r-1}\left\{ \frac{r({{r}^{n}}-1)}{r-1}-n \right\}\] \[\Rightarrow \] \[(r-1){{U}_{n}}=\frac{ar({{r}^{n}}-1)}{r-1}-an\] \[\Rightarrow \] \[r{{S}_{n}}+(1-r){{U}_{n}}=an\]You need to login to perform this action.
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