A) \[nA-(n-1)l\]
B) \[nA-l\]
C) \[{{2}^{n-1}}A-(n-1)l\]
D) \[{{2}^{n-1}}A-l\]
Correct Answer: A
Solution :
Given\[,\] \[{{A}^{2}}=2A-l\] ? (i) On multiplying by \[A\] both sides, we get \[{{A}^{2}}\cdot A=(2A-l)A\] \[\Rightarrow \] \[{{A}^{3}}=2{{A}^{2}}-lA\] \[=2(2A-l)-lA\] [from Eq. (i)] \[=4A-2l-A\] \[(\because \,\,lA=A)\] \[=3A-2l\] Similarly,\[{{A}^{4}}=4A-3l\] \[{{A}^{5}}=5A-4l\] Hence, \[{{A}^{n}}=nA-(5-1)l\]You need to login to perform this action.
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