A) 12
B) 13
C) 14
D) 15
Correct Answer: D
Solution :
\[(1+r)(1+{{r}^{2}})(1+{{r}^{4}})(1+{{r}^{8}})\] \[=(1+r+{{r}^{2}}+{{r}^{3}})(1+{{r}^{4}})(1+{{r}^{8}})\] \[=(1+r+{{r}^{2}}+{{r}^{3}}+{{r}^{4}}+{{r}^{5}}+{{r}^{6}}+{{r}^{7}})(1+{{r}^{8}})\] \[=1+r+{{r}^{2}}+....+{{r}^{11}}+{{r}^{12}}+{{r}^{13}}+{{r}^{14}}+{{r}^{15}}\] Thus for \[x=15,\,\]the equation \[1+r+{{r}^{2}}+....+{{r}^{x}}\] \[=(1+r)(1+{{r}^{2}})(1+{{r}^{4}})(1+{{r}^{8}})\]holds.You need to login to perform this action.
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