A) \[{{2}^{n}}\]
B) \[{{3}^{n}}\]
C) \[{{3}^{n}}-1\]
D) \[{{3}^{n}}+1\]
Correct Answer: C
Solution :
[c] Given series is \[^{n}{{C}_{1}}\times {{2}^{1}}{{+}^{n}}{{C}_{2}}\times {{2}^{2}}{{+}^{n}}{{C}_{3}}\times {{2}^{3}}+....{{+}^{n}}{{C}_{n}}\times {{2}^{n}}\] \[=[1{{+}^{n}}{{C}_{1}}\times {{2}^{1}}{{+}^{n}}{{C}_{2}}\times {{2}^{2}}{{+}^{n}}{{C}_{3}}\times {{2}^{3}}+....{{+}^{n}}{{C}_{n}}\times {{2}^{n}})-1\]\[={{(1+2)}^{n}}-1={{3}^{n}}-1\]You need to login to perform this action.
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