If n∈N, n$$1$$, then value of $$E=a$$−$$nC1(a$$−$$1)+nC2(a$$−$$2)+$$…$$+($$−$$1)n(a$$−$$n)$$ nCn is

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If n∈N, n>$$1$$, then value of $$E=a$$−$$nC1(a$$−$$1)+nC2(a$$−$$2)+$$…$$+($$−$$1)n(a$$−$$n)$$ nCn is

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We can write E asa $$nC0$$−$$nC1+nC2$$−…$$+($$−$$1)n$$ $$nCn+$$ $$nC1$$− (2)  $$nC2+(3)$$ $$nC3$$−…−$$($$−$$1)n(n)$$ nCn    $$=0+F$$ $$whereF=$$ $$nC1$$−(2) $$nC2+(3)$$ $$nC3$$−…−  $$($$−$$1)n(n)$$ nCn       We have (1+x)n=nC0+nC1x+nC2x2+nC3x3+$$…$$+nCnxnDifferentiating$$, we get   $$n(1+x)n$$−$$1=nC1+2$$ $$nC2x+3$$ $$nC3x2+$$…$$+n$$ nCnxn−$$1Putting$$ $$x=-1$$, we get          $$0=nC1$$−$$2$$ $$nC2+3$$ $$nC3$$−…−$$($$−$$1)n$$−$$1(n) nCn⇒ $$0=FThus$$,     $$E=0+0=0$$.

If $n \in N, n > 1$ , then value of $E = a -^{n} C_{1} (a - 1) +^{n} C_{2} (a - 2) + \dots + (- 1)^{n} (a - n) (^{n} C_{n})$ is

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If n∈N, n>1, then value of E=a−nC1(a−1)+nC2(a−2)+…+(−1)n(a−n) nCn is

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If $n \in N, n > 1$ , then value of $E = a -^{n} C_{1} (a - 1) +^{n} C_{2} (a - 2) + \dots + (- 1)^{n} (a - n) (^{n} C_{n})$ is