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If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n the...

If `(1+x)^n = ^nC_0+ ^nC_1x+…….+^nC_nx^n` then find `^nC_0//2+^nC_1//3+^nC_2//4+……+^nC_n//(n+2)`

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. (1+x)^n=^nC0+^nC1x+^nC2x^2+……….+^nCnx^n then find the value of ^nC0 + ...

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  2. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find the value of ^nC0//1+^n...

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  3. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find ^nC0//2+^nC1//3+^nC2//4...

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  4. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find ^nC0 ^nCr +^nC1 ^nC(r-1...

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  5. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find ^nC0 ^2+ ^nC1 ^2 +^nC2^...

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  6. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find the value of ^nC1 ^2+2^...

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  7. Let R=(5 sqrt 5+11)^(2n+1) and f=R-[R] where [] is the greatest intege...

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  8. Last three digit of 27^(27)

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  9. Find remainder when 7^(103) is divided by 25.

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  10. If n in I^+ show 2^(3n+3) -7n -8 is divisible by 49.

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  11. Find the coefficient of x^7 in (1+3x-2x^3)^10

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  12. Find the coefficient of a^3b^4c^5 in (ab+bc+ca)^6

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  13. Expand (x^2+(3/x))^4 , xne0

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  14. Compute (98)^5

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  15. Using binomial theorem prove that 6^n-5n always leaves remainder I whe...

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  16. Find a, if 17th and 18th terms in the expansions of (2+a)^50 are equal...

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  17. Find the coefficient of x^6y^3 in the expansion of (x+2y)^9

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  18. Use the principle of mathematical induction to show that 5^(2+1)+3^(n+...

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  19. Prove by mathematical induction that sum(r=0)^n "^nCr = n cdot 2^(n-1)

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  20. For ninN, prove that ((n+1)/2)^ngt n!

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