Q.If $(1 + x)^{20} + (1 + x)^{21} + \cdots + (1 + x)^{30} = \sum_{r=0}^{k} a_r x^r$ , then $a_0 + a_1 + a_2 + \cdots + a_{10}$ equals

11 \cdot 2^{30}

\dfrac{11}{2} (2^{31} - 1)

11 \cdot 2^{30} - 11

\dfrac{11}{2} (2^{31} + 1)

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

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Q.If (1+x)20+(1+x)21+⋯+(1+x)30=∑r=0karxr(1 + x)^{20} + (1 + x)^{21} + \cdots + (1 + x)^{30} = \sum_{r=0}^{k} a_r x^r(1+x)20+(1+x)21+⋯+(1+x)30=∑r=0k​ar​xr, then a0+a1+a2+⋯+a10a_0 + a_1 + a_2 + \cdots + a_{10}a0​+a1​+a2​+⋯+a10​ equals