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If ak=1/(k(k+1)) for k=1 ,2……..,n then p...

If `a_k=1/(k(k+1))` for k=1 ,2……..,n then prove that `(sum_(k=1)^n a_k)^2 =n^2/(n+1)^2`

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Find the last three digits of (17)^256

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  2. Find the term independent of x in the expansion of [(t^(-1)-1)x+(t^(-1...

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  3. If ak=1/(k(k+1)) for k=1 ,2……..,n then prove that (sum(k=1)^n ak)^2 =n...

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  4. Find the unit digit in the number 17^(1995)+11^(1995)-7^(1995)

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  5. If ((1+x)/(1-x))^n=1+a1x+a2x^2+…….+arx^r+…….. then prove that a1+a2+a3...

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  6. Prove that ^nC0 "^(2n)Cn-^nC1 ^(2n-2)Cn +^nC2 ^(2n-4)Cn =2^n

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  7. If (1+x)^n=a0+a1x+a2x^2+…….+anx^n then prove that (1+(a/a0))(1+(a2)/(a...

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  8. Prove that the following identity about binomial coefficients ((n),(0)...

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  9. The terms independent of x in (3/2(x^2)-1/(3x))^9 is

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  10. The 10^(th) term in the expansion of (2x^2+1/x)^(12) is

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  11. If the 6th term in the expansion of (1/x^(8//3)+x^2log(10)x)^8 is 5600...

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  12. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is

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  13. The sum of series ,^20C0-^20C1+^20C2-^20C3+.....+ ^20C10 is

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  14. ^8C2+^8C3+^8C4+....^8C7 is equal to

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  15. .^18C15+2(.^18C16)+^17C16+1=^nC3, then n is equal to

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  16. The value of 1^2cdotC1+3^2cdotC3+5^2cdotC5+......, is

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  17. Let [x] denotes the greatest integer less then or equal to x. If x=(sq...

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  18. The fractional part of =(2^(4n))/15 is

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  19. If p=(8+3sqrt7)^n and f=p-[p], where [.] denotes the greatest integer ...

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  20. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is

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