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Q.If (1+x)2n+1=∑r=02n+1crxr(1 + x)^{2n+1} = \sum_{r=0}^{2n+1} c_r x^r, then c0+c3+c6+⋯c_0 + c_3 + c_6 + \cdots equals

a
4n+(−1)n3\dfrac{4^{n} + (-1)^{n}}{3}
b
4n+1+(−1)n3\dfrac{4^{n+1} + (-1)^{n}}{3}
c
4n+1+2⋅(−1)n3\dfrac{4^{n+1} + 2 \cdot (-1)^n}{3}
d
4n+2⋅(−1)n3\dfrac{4^{n} + 2 \cdot (-1)^n}{3}

Correct Answer: Option C

The correct solution involves applying the fundamental concept to derive the final value step by step...

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