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The number 51^(49)+51^(48)+51^(47)+........

The number `51^(49)+51^(48)+51^(47)+........+51+1` is divisible by a. 10 b. 20 c. `25` d. `50`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
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  2. Each question has four choices a, b, c and d, out of which only one is...

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  3. The number 51^(49)+51^(48)+51^(47)+........+51+1 is divisible by a. 10...

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  4. If sum(r=0)^(n) (r)/(""^(n)C(r))= sum(r=0)^(n) (n^(2)-3n+3)/(2.""^(n)C...

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  5. If (1+x)^n=C0+C1x+C2x^2+.......+Cn x^n , then show that the sum of th...

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  6. For any positive integer (m,n) (with ngeqm), Let ((n),(m)) =.^nCm Prov...

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  7. If sum(r=0)^n{ar(x-alpha+2)^r-br(alpha-x-1)^r}=0, then prove that bn-(...

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  8. Let a=(2^(1//401)-1) and for each ngeq2,l e tbn=^n C1+^n C2dota+^n C3...

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  9. Prove that sum(r=0)^n^n Cr(-1)^r[i^r+i^(2r)+i^(3r)+i^(4r)]=2^n+2^(n/2+...

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  10. Find the coefficient of x^n in (1+x/(1!)+(x^2)/(2!)+........+(x^n)/(n ...

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  11. Prove that (^n C0)/x-(^n C0)/(x+1)+(^n C1)/(x+2)-+(-1)^n(^n Cn)/(x+n)=...

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  12. If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(...

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  13. Given, sn=1+q+q^2+.....+q^n ,Sn=1+(q+1)/2+((q+1)/2)^2+...+((q+1)/2)^n...

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  14. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be a. x^n b. x^(-...

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  15. sum(k=1)^ook(1-1/n)^(k-1)=>? a.n(n-1) b. n(n+1) c. n^2 d. (n+1)^2

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  16. The coefficient of x^4 in the expansion of {sqrt(1+x^2)-x}^(-1) in asc...

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  17. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to a. x...

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  18. The value of sum(r=1)^(15)(r2^r)/((r+2)!) is (a).((17)!-2^16)/((17)!) ...

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  19. (n+2)C0(2^(n+1))-(n+1)C1(2^(n))+(n)C2(2^(n-1))-.... is equal to

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  20. The value of sum(r=0)^(50)(-1)^r((50)Cr)/(r+2) is equal to a . 1/(50x...

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