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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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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the remainder when 5^(99) is divided by 13.

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

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

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  4. If the coefficient of the middle term in the expansion of (1+x)^(2n+2)...

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  5. If the coefficients of three consecutive terms in the expansion of (1+...

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  6. In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...

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  7. Prove that (C0+C1)(C1+C2)(C2+C3)(C3+C4)...........(C(n-1)+Cn) = (C0...

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  8. If the coefficients of four consecutive terms in the expansion of (1+x...

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  9. Find the sum of sum(r=1)^n r* (nCr)/(nC(r-1)

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  10. Find the positive integer just greater than (1+0. 0001)^(10000)dot

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  11. Find the last digit of 17^(256)dot

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  12. If 10^m divides the number 101^(100)-1 then, find the greatest value o...

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  13. Using the principle of mathematical induction, prove that (2^(3n)-1) i...

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  14. If x is very large as compare to y , then prove that sqrt(x/(x+y))dot...

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  15. Find the coefficient of x^n in the expansion of (1-9x+20 x^2)^(-1)dot

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  16. Prove that the coefficient of x^r in the expansion of (1-2x)^(-1/2) is...

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  17. Find the sum: 1-1/8+1/8xx3/(16)-(1xx3xx5)/(8xx16xx24)+...

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  18. Show that sqrt3 =1+1/3+(1/3).(3/6)+(1/3).(3/6).(5/9)+.......

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  19. Assuming x to be so small that x^2 and higher power of x can be neg...

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

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