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

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If the coefficients of four consecutive terms in the expansion of (1+x...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Find the condition for which the formula (a+b)^m = a^m+m a^(m-1)b+(m(...

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  15. Find the value of x , for which 1/(sqrt(5+4x)) can be expanded as infi...

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  16. Find the fourth term in the expansion of (1-2x)^(3//2)""dot

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

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  18. Prove that ^n C0 .^n C0-^(n+1)C1 . ^n C1+^(n+2)C2 . ^n C2-=(-1)^ndot

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  19. The sum of the coefficients of all the integral powers of x in the exp...

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  20. If the sum of the coefficient in the expansion of (alpha^2x^2-2alphax+...

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