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The sum of the series ""^20C0 - ""^20C1 ...

The sum of the series `""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10` is

A

`""^20C_10`

B

`- (""^20C_10)`

C

`1/2. (""^20C_10)`

D

`0`

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The correct Answer is:
C
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""^20C_0 + ""^20C_1 + ""^20C_2+…….+""^20C_10 =

1.""^20C_1 - 2.""^20C_2 + 3.""^20C_3 - …..-20.""^20C_20 =

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

Prove that (""^20C_1)/(""^20C_0) + 2. (""^20C_2)/(""^20C_1) + 3. (""^20C_3)/(""^20C_2) + …..+20. (""^20C_20)/(""^20C_19) = 210

""^20C_10.""^15C_0 + ""^20C_9.""^15C_1 + ""^20C_8.""^15C_2 + …..+""^20C_0.""^15C_10 =

(""^(20)C_(1))/(""^(20)C_(0))+2.(""^(20)C_(2))/(""^(20)C_(1))+3.(""^(20)C_(3))/(""^(20)C_(2)) +…20.(""^(20)C_(20))/(""^(20)C_(19)) =210

1,2,3…..sum of 20 term is

AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. ""^(n) C(r+1)+2""^(n)C(r) +""^(n)C(r-1)=

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  2. If Ck is the coefficient of x^k in the expansion of (1 + x)^2005 and i...

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  3. The sum of the series ""^20C0 - ""^20C1 + ""^20C2 - ""^20C3 +…….""^20C...

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  4. If S(n) = underset (r=0) overset( n) sum (1) /(""^(n) C(r)) and T...

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  5. C0 - [C1 -2.C2+ 3.C3-……..+(-1)^(n-1).n.Cn] =

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  6. C0+4. C1 + 7. C2+…...(n+1) terms =

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  7. 2. C2 + 6. C3 + 12. C4 +….. + n (n-1) . Cn=

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  8. Sum of last 8 coefficients in (1 + x)^16 is

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  9. C0 + (C1)/(2) (4) + (C2)/(3) (16) + …………..+(Cn)/(n + 1) (2^(2n))

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  10. (1 +x)^15 = a0 + a1x +…..+a15 x^15 rArr sum(r = 1)^15 r (ar)/(a(r - 1)...

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  11. The value of sum(r = 1)^15 r^2 ((""^15Cr)/(""^15C(r - 1)) ) of is equa...

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  12. If ak is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k...

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  13. Find the sum of the following (""^(15)C(1))/(""^(15)C(0))+2(""^(15)C...

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  14. If a0, a1 , a2 …..an are binomial coefficients then (1 + a1/a0)(1 +a2/...

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  15. ((C0 + C1)(C1 + C2)(C2 + C3)………(C(n-1) + Cn) )/(C0C1C2…Cn)

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  16. If (1+x)(1+x+x^2)(1+x+x^2+x^3)……(1+x+x^2+……+x^(n-1)) = a0 + a1x + a2x^...

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  17. If (1 -x + x^2)^n = a0 +a1x + a2x^2+….+a(2n)x^(2n) then a0 + a2 +a4 +...

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  18. If (1)/(1!(n-1)!) + (1)/(3!(n-3)!) + (1)/(5!(n-5)!) +…. =

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  19. C0 + C1 + 2.C2(3) + 3.C3(3^2)+ 4.C4(3^3) + ……+n.Cn 3^(n-1) =

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  20. (1 + x+x^2)^8 = a0 + a1x +…….+a16 x^16 then a0 - a2 + a4 - a6 + ……..+a...

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