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

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

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Prove that the coefficient of x^r in the expansion of (1-2x)^(-1/2) is...

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

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

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

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

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

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

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

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

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

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

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

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  13. Prove that sum(alpha+beta+gamma = 10) (10 !)/(alpha!beta!gamma!)=3^(10...

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  14. If (1+x-2x^2)^(20)=a0+a1x+a2x^2+a3x^3+...+a(40)x^(40), then find the v...

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  15. Find the sum of the series .^15 C0+^(15)C1+^(15)C2+...............+^(1...

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  16. Find the sum sum(k=0)^(10).^(20)Ck.

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  17. Find the sum of all the coefficients in the binomial expansion of (x^2...

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  18. If the sum of coefficient of first half terms in the expansion of (x+y...

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  19. Find the value of underset(p=1)overset(n)sum(underset(m=p)overset(n)su...

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  20. Show that the middle term in the expansion of (x+1)^(2n) is (1.3.5.......

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