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Using binomial theorem prove that 6^n-5n...

Using binomial theorem prove that `6^n-5n` always leaves remainder I when divided by 25.

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Expand (x^2+(3/x))^4 , xne0

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  2. Compute (98)^5

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

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

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

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

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

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

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  9. Using mathematical induction to show that p^(n+1) +(p+1)^(2n-1) is div...

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  10. Prove by induction that the integer next greater than (3+sqrt5)6n is d...

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  11. Using the principle of mathematical induction show that tan^(-1)(x/(1+...

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

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

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

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

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

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

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

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  19. 5th term from the end in the expansion of ((x^3/2)-(2/x^2))^12 is

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

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