Question : The value of $[(0.87)^2+(0.13)^2+(0.87)×(0.26)]^{2013}$ is:
Option 1: 0
Option 2: 2013
Option 3: 1
Option 4: –1
Correct Answer: 1
Solution : Given: $[(0.87)^2+(0.13)^2+(0.87)×(0.26)]^{2013}$ = $[(0.87)^2+(0.13)^2+(0.87)×2×(0.13)]^{2013}$ = $(0.87+0.13)^{2\times 2013}$ = $(1)^{2\times 2013}$ = $1$ Hence, the correct answer is 1.
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