Q57 / 160 · AP EAMCET 2025 (21 MAY SHIFT 1) · Mathematics

If $(1+x)^n=\sum_{r=0}^n C_r x^r$, then the value of $C_0+\left(C_0+C_1\right)+\left(C_0+C_1+C_2\right)+\ldots+$ $\left(\mathrm{C}_0+\mathrm{C}_1+\mathrm{C}_2+\ldots+\mathrm{C}_{\mathrm{n}}\right)$ is

  • A
    $\mathrm{n} 2^{\mathrm{n}-1}$
  • B
    $2^{\mathrm{n}}+\mathrm{n}$
  • C
    $(\mathrm{n}+2) 2^{\mathrm{n}}$
  • Correct answer
    D
    $(\mathrm{n}+2) 2^{\mathrm{n}-1}$

Hence, the correct answer is option: 'D'.

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