{C_0} - {C_1} + {C_2} - {C_3} + ..... + {( - | vedclass

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Question

(c) We know that${(1 + x)^n} = {\,^n}{C_0} + {\,^n}{C_1}x + {\,^n}{C_2}{x^2} + .... + {\,^n}{C_n}{x^n}$

Putting $x = -1$, we get ${(1 - 1)^n} = {\,

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$0$

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(c) We know that${(1 + x)^n} = {\,^n}{C_0} + {\,^n}{C_1}x + {\,^n}{C_2}{x^2} + .... + {\,^n}{C_n}{x^n}$

Putting $x = -1$, we get ${(1 - 1)^n} = {\,^n}{C_0} - {\,^n}{C_1} + {\,^n}{C_2} - .....{( - 1)^{n\,\,n}}{C_n}$

Therefore ${C_0} - {C_1} + {C_{_2}} - {C_3} + ....( - 1){\,^n}{C_n} = 0$

${C_0} - {C_1} + {C_2} - {C_3} + ..... + {( - 1)^n}{C_n}$ is equal to

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