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The remainder, if 1+2+2^2+2^3+....+2^199...

The remainder, if `1+2+2^2+2^3+....+2^1999` in divided by 5 is

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Given (1-2x+5x^2-10x^3)(1+x)^n=1+a1x+a2x^2+.... and that a1^2=2a2, the...

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  2. The digit in the units place of the decimal representation of 7^1000 i...

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  3. The remainder, if 1+2+2^2+2^3+....+2^1999 in divided by 5 is

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  4. The sum of possible values of x for which the fifth term in the expans...

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  5. Find the coefficient of x^24 in (x^2+(3a)/x)^15

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  6. If in the expansion of (1+x)^43 the coefficient of (2r+1)^(th) term in...

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  7. The coefficient of the middle term of the expansion of (1-2x+x^2)^n is

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  8. Find the coefficient of x^4 in the expansion of (1+x-2x^2)^7

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  9. If the coefficients of four consecutive terms in the expansion of (1+x...

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  10. If (1+x)^n=sum(r=0)^nCrx^r prove that (2^2C0)/(1 . 2)+(2^3C1)/(2 . 3)+...

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  11. If p+q=1, then show that sum(r=0)^nr^2^nCrp^rq^(n-r)=npq+n^2p^2

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  12. Prove that C1+C5+C9+....=1/2(2^(n-1)+2^(n//2)sin((npi)/4))

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  13. Prove that C1+C4+C7+....=1/3[2^n-2cos((n+1)/3pi)]

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  14. Prove that (2nC0)^2-(2nC1)^2+(2nC2)^2+.....+(2nC2n)^2=(-1)^n2nCn

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  15. The coefficient of x^9 in the expansion of (1+x)(1+x^2)(1+x^3)....(1+x...

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  16. The sum of coefficient of integral powers of x in the binomial expansi...

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  17. Number of irrational terms in the binomial expansion of (3^(1//5)+7^(1...

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  18. Coefficient of x^11 in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^12 i...

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  19. Let S=2/1^nC0+2^2/2^nC1+2^3/3^nC2+....+2^(n+1)/(n+1)^nCn. Then S equal...

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  20. The coefficient of x^3 in the infinite series expansion of 2/((1-x)(2-...

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