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Use induction to prove that 3^(2n)-1 is ...

Use induction to prove that `3^(2n)-1` is not exactly divisible by `2^(n+3)` for an `ninN`

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Using the principle of mathematical induction show that tan^(-1)(x/(1+...

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  2. Prove by induction that (1+x1)(1+x2)(1+x3)…….(1+xn) ge 1+x1+x2+……+xn

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  3. Use induction to prove that 3^(2n)-1 is not exactly divisible by 2^(n+...

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  4. (x+sqrt(x^3-1))^5+(x-sqrt(x^3-1))^5 is a polynomial of degree

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  5. if the coefficients of x^7 & x^8 in the expansion (2+x/3)^n are equal ...

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  6. The term independent of x in (sqrt(x/3)+sqrt(3/(2x^2)))^10 is

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  7. The total number of terms in the expansion of (x+y)^(100)+(x-y)^(100) ...

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  8. The term independent of x in the expansion of (1+x+2x^3)(3/2(x^2)-1/(3...

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  9. 5th term from the end in the expansion of ((x^3/2)-(2/x^2))^12 is

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  10. The coefficient of x^3 in the expansion of (1-x+x^2)^5 is

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  11. The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is

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  12. The greatest term (numerically) in the expansion of (3-5x)^11 when x=1...

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  13. Which of the following expression is divisible by 1225?

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  14. The value of where ^nCr is

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  15. If the sum of odd numbered terms and the sum of even numbered terms in...

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  16. If P(n)=2+4+6+…..+2n ninN then P(k) =k(k+1) implies P(k+1)=(k+1)(k+2) ...

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  17. The value of the natural numbers n such that the inequality 2^ngt2n+1 ...

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  18. When P is a natural number then p^(n+1)+(p+1)^(2n-1) is divisible by

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  19. Let P(n) denote the statement that n^2+n is odd. It is seen that P(n) ...

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  20. For a positive integer n let a(n)=1+1/2+1/3+1/4+….+1/((2^n)-1) Then

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