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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)*(7/12)+.......

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Show that 1 + 1/3 + (1.3)/(3.6) + (1.3.5)/(3.6.9) + ….. = sqrt3

Show that 1 + 1/2.(3/5) + (1.3)/(2.4) (3/5)^2 + (1.3.5)/(2.4.6) (3/5)^3 + …… = sqrt([5/2])

(1)/(1.2.3)+(1)/(3.4.5)+(1)/(5.6.7)+....

1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+.....oo

(1)/(1.2)+(1)/(3.4)+(1)/(5.6)+....

Show that + 1/4 + (1.3)/(4.8) + (1.3.5)/(4.8.12) + …….= sqrt2

Evaluate: (1/2)^3+\ (1/3)^3-\ \ (5/6)^3

Show that 1 - 3/4 + (3.5)/(4.8)- (3.5.7)/(4.8.12)+……..= sqrt((8/27))

The sum of the infite series (1/3)^(2)+1/3(1/3)^(4)+1/5(1/3)^(6) +……..is

Solve (a) 2/3 + 1/7 (b) 3/10 + 7/15 (c) 4/9 + 2/7 (d) 5/7 + 1/3 (e) 2/5 + 1/6 (f) 4/5 + 2/3 (g) (3/4) (1/3) (h) (5/6) (1/3) (1) 2/3 + 3/4 + 1/2 (1) 1/2 + 1/3 = 1/6 (k) (1) 1/3 + (3) 2/3 (1) (4) 2/3 +(3) 1/4 (m) ((16)/5))(7/5)

CENGAGE ENGLISH-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)*(7/12)+.......

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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)j^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 .^n C0 . ^(2n) Cn- ^n C1 . ^(2n-2)Cn+^n C2 . ^(2n-4)Cn-=2...

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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. Find the sum of the coefficients of all the integral powers of x in th...

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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 sum(p=1)^n(sum(m=p)^n.^nCm.^m Cp)dot And hence, find...

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  20. Show that the middle term in the expansion of (1+x)^(2n)i s((1. 3. 5 (...

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