If n-2 then a-1-C1-a-2-C2-a-3-C3-1n-1a-n-Cn-

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Sum of Coefficients of All Terms

If n≥2 then...

Question

If $n \geq 2$ then $(a - 1) . C_{1} - (a - 2) . C_{2} + (a - 3) . C_{3} - \dots \dots (- 1)^{n - 1} (a - n) . C_{n} =$

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\frac{C_{1}}{C_{0}} + 2. \frac{C_{2}}{C_{1}} + 3. \frac{C_{3}}{C_{2}} + . . . . . + n . \frac{C_{n}}{C_{n - 1}}

n \geq 2

3. C_{1} - 4. C_{2} + 5. C_{3} - . . . . . . + {(- 1)}^{n - 1} (n + 2) . C_{n}

c_{0}, c_{1}, c_{2}, . . . . . . c_{n}

(1 + x)^{n},

n

c_{1} - \frac{c_{2}}{2} + \frac{c_{3}}{3} - . . . . . . + \frac{(- 1)^{n - 1} c_{n}}{n} = 1 + \frac{1}{2} + \frac{1}{3} + . . . . \frac{1}{n}

\frac{C_{1}}{1} - \frac{C_{2}}{2} + \frac{C_{3}}{3} - \frac{C_{4}}{4} + . . . . . + \frac{(- 1)^{n - 1}}{n} C_{n}

= 1 + \frac{1}{2} + \frac{1}{3} + . . . . . + \frac{1}{n} .

C_{n}

x^{n}

(1 + x)^{n}

C_{1} + 2. C_{2} + 3. C_{3} + \dots + n . C_{n} =

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