If 1 - x n - C 0 - C 1 x - C 2 x 2 - - - C x 2 prove that C0-C1-C2- -Cn-2n

(1+x)^n=C_0+C_1x+⋯+Cx^n Put x=1 (1+1)^n=C_0+C_1(1)+⋯+C(1)^n 2^n=C_0+C_1+⋯+C_n ...

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Byju's Answer

Standard XII

Mathematics

Combination

If 1 + x n...

Question

If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C x^{2}$ prove that
$C_{0} + C_{1} + C_{2} + \dots + C_{n} = 2^{n}$

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Solution

$(1 + x)^{n} = C_{0} + C_{1} x + \dots + C x^{n}$
Put $x = 1$
$(1 + 1)^{n} = C_{0} + C_{1} (1) + \dots + C (1)^{n} 2^{n} = C_{0} + C_{1} + \dots + C_{n}$

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If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . . + C_{n} x^{n}$ , then $\frac{C_{1}}{C_{0}} + \frac{2 C_{2}}{C_{1}} + \frac{3 C_{3}}{C_{2}} + . . . . . . . . + \frac{n C_{n}}{C_{n - 1}} =$

Q. If

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

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Q. If

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

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If (1+x)n=C0+C1x+C2x2+…+Cx2 prove thatC0+C1+C2+⋯+Cn=2n

(1+x)n=C0+C1x+⋯+CxnPut x=1(1+1)n=C0+C1(1)+⋯+C(1)n2n=C0+C1+⋯+Cn

If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C x^{2}$ prove that
$C_{0} + C_{1} + C_{2} + \dots + C_{n} = 2^{n}$

$(1 + x)^{n} = C_{0} + C_{1} x + \dots + C x^{n}$
Put $x = 1$
$(1 + 1)^{n} = C_{0} + C_{1} (1) + \dots + C (1)^{n} 2^{n} = C_{0} + C_{1} + \dots + C_{n}$