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Find the value of .^(4n)C0+^(4n)C4+^(4n)...

Find the value of `.^(4n)C_0+^(4n)C_4+^(4n)C_8+...+""^(4n)C_(4n)` .

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Find the following sums : (i) .^(n)C_(0)-.^(n)C_(2)+.^(n)C_(4)-.^(n)C_(6)+"....." (ii) .^(n)C_(1)-.^(n)C_(3)+.^(n)C_(5)-.^(n)C_(7)+"...." (iii) .^(n)C_(0)+.^(n)C_(4)+.^(n)C_(8)+.^(n)C_(12)+"....." (iv) .^(n)C_(2) + .^(n)C_(6) + .^(n)C_(10)+.^(n)C_(14)+"......" (v) .^(n)C_(1) + .^(n)C_(5)+.^(n)C_(9)+.^(n)C_(13)+"...." (vi) .^(n)C_(3) + .^(n)C_(7) + .^(n)C_(11) + .^(n)C_(15) + "....."

If ""^(n)C_(9)=""^(n)C_(8) , find ""^(n)C_(17) .

The value of (""^(n) C_(1)+2. ""^(n) C_(2)+3. ""^(n)C_(3)+…+ n""^(n)C_(n)) is-

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n)

If .^(n)C_(5)=.^(n)C_(3) , then find .^(n)C_(4) .

If .^(n)C_(4)=.^(n)C_(2) , then find .^(n)C_(3) .

If .^(n)C_(5)=.^(n)C_(4) , then find .^(n)C_(7) .

If .^(n)C_(4)=.^(n)C_(6) , then find .^(n)C_(9) .

Find the value of n such that (""^(n)P_(4))/(""^(n-1)P_(4))=(5)/(3), n gt 4

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  2. Using the binomial theorem (without using the formula for .^(n)C(r)), ...

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  3. Find the value of .^(4n)C0+^(4n)C4+^(4n)C8+...+""^(4n)C(4n) .

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  4. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

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  5. Find the coefficient of x^(n) in the polynomial (x+.^(n)C(0)) (x+3.^(n...

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  6. If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the sum of C1+2C3+3...

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  7. Prove that (.^n C0)/1+(.^n C2)/3+(.^n C4)/5+(.^n C6)/7+ . . . =(2^n)/(...

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  8. Find the sum sumsum(0lt=i<jlt=n-1)^n Cidot

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  9. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1), as...

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  10. Prove that (1^2)/3""^n C1+(1^2+2^2)/5""^n C2+(1^1+2^2+3^2)/7""^n C3+.....

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  11. Prove that (1)/(n+1)=(.^(n)C(1))/(2)-(2(.^(n)C(2)))/(3)+(3(.^(n)C(3)...

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  12. Find the sum 2..^(10)C(0) + (2^(2))/(2).^(10)C(1) + (2^(3))/(3).^(1...

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  13. If in the expansion of (2x+5)^(10) , the numerically greatest term in ...

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  14. Find the value of (1)/(81^(n))-(10)/(81^(n)).^(2n)C(1) + (10^(2))/(8...

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  15. Find the value of 5C3 + 4C2

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  16. Find the sum .^1C0+^2C1+^3C2+....+^(n+1)Cn ,where Cr=^n Crdot

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  17. If (1+x+x^(2) + "……" + x^(n))^(n) = a(0) + a(1)x+a(2)x^(2) + "….." a(n...

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  18. If n gt 2, then prove that C(1)(a-1) - C(2) xx (a-2) + "….." + (-1)^(...

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  19. Find the sum C0-C2+C4-C6+ ......... ,where Cr=^n Cr .

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  20. If x+y=1, prove that sum(r=0)^n .^nCr x^r y^(n-r) = 1.

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