2C0 - 22 C12 - 23 C23 - 24 C34 - -2n-1Cnn-1- 3n-1-1n-1

2C_0 + 2^2 C_12 + 2^3 C_23 + #160; 2^4 C_34 + .........+2^n+1C_nn+1= 3^n+1 1n+1 =∑_r=0^n^nC_rr+12^r 1 = 1n+1 ∑_r = 0^n n+1r+1 ^ ...

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Combination

2C0 + 22 C12 ...

Question

$2 C_{0} + 2^{2} \frac{C_{1}}{2} + 2^{3} \frac{C_{2}}{3} + 2^{4} \frac{C_{3}}{4} + . . . . . . . . . + 2^{n + 1} \frac{C_{n}}{n + 1} = \frac{3^{n + 1} - 1}{n + 1}$

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Similar questions

2 C_{0} + \frac{C_{1}}{2} \cdot 2^{2} + \frac{C_{2}}{3} \cdot 2^{3} + \frac{C_{3}}{4} \cdot 2^{4} + \dots + \frac{C_{n}}{n + 1} \cdot 2^{n + 1}

(C_{r} =^{n} C_{r})

^{2 n + 1} C_{0} +^{2 n + 1} C_{1} +^{2 n + 1} C_{2} + . . . . . . +^{2 n + 1} C_{n} +^{2 n + 1} C_{n + 1} +^{2 n + 1}

C_{n + 2} + . . . . . +^{2 n + 1} C_{2 n + 1}

n = 3

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{n} x^{n},

\sum \sum 0 \leq r < s \leq n (r + s) C_{r} C_{s}

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . C_{n} x^{n}

3 C_{0} + 3^{2} \frac{C_{1}}{2}

\frac{3^{3} C_{2}}{3} + \frac{3^{4} C_{3}}{4}

\frac{3^{n + 1} C_{n}}{n + 1}

\frac{4^{n + 1} - 1}{n + 1}

C_{0} + 2 \cdot C_{1} + 3 \cdot C_{2} + . . . . . + (n + 1) C_{n} = 2^{n - 1} \cdot (n + 2)

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