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Show that (4)/(12.18) - (4.7)/(12.18.2...

Show that `(4)/(12.18) - (4.7)/(12.18.24) + (4.7.10)/(12.18.24.30) - …..= 3 root(3) (9/4) - 47/12`

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Show that (5)/(6.12) + (5.8)/(6.12.18) + (5.8.11)/(6.12.18.24) + ….. = (3root(3)(4) -4)/(6)

Show that (3)/(4.8)-(3.5)/(4.8.12) + (3.5.7)/(4.8.12.16) - …… = sqrt(2/3) -3/4

(5)/(6.12)+(5.8)/(6.12.18)+(5.8.11)/(6.12.18.24)+…....=

Show that 3/4 + (3.5)/(4.8)+ (3.5.7)/(4.8.12)+ …… = sqrt8 -1

(4)/(1.3)-(6)/(2.4)+(12)/(5.7)-(14)/(6.8)+….=

(3)/(4.8)+(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)+….=

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

(1)/(4)-(5)/(4.8)+(5.7)/(4.8.12)-…....=

AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. Show that (4.6)/(5.10) + (4.6.8)/(5.10.15) + (4.6.8.10)/(5.10.15.20) +...

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  2. Show that (5)/(6.12) + (5.8)/(6.12.18) + (5.8.11)/(6.12.18.24) + ….. =...

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  3. Show that (4)/(12.18) - (4.7)/(12.18.24) + (4.7.10)/(12.18.24.30) -...

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  4. If x = (1.3)/(3.6) + (1.3.5)/(3.6.9) + (1.3.5.7)/(3.6.9.12) + ….. th...

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  5. If t = 1 - 1/8 + (1.3)/(8.16) -(1.3.5)/(8.16.24) + …… then prove that ...

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  6. If n is a non zero rational number then show that 1 + n/2 + (n (...

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  7. Prove that : Find the 7^("th") term in the expansion of ((4)/(x^(3))+(...

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  8. Prove that : Find the 3^("rd") term from the end in the expansion of (...

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  9. Prove that : Find the coefficient of x^(9) and x^(10) in the expansion...

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  10. Prove that : Find the term independent of x (that is the constant ter...

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  11. Prove that : If the coefficients of (2r+4)^("th") and (r-2)^("nd") te...

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  12. Find the numerically greatest terms in the expansion of (2x +3x)^...

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  13. Find the numerically greatest terms in the expansion of (3x-4y)^(14...

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  14. Prove that : Suppose that n is a natural number and I, F are respecti...

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  15. Prove that : Find the coefficient of x^(6) in (3+2x+x^(2))^(6).

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

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  17. Find the number of terms free of radical sign in (5^(1//2) +7^(1//5))^...

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  18. Show that the coefficient of x^(k) (0 le k le n) in the expansion of ...

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  19. For natural numbers m, n if (1-y)^m (1+y)^n=1+a1 y +a2 y^2 + …, and a1...

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  20. Prove that : Find the coefficient of x^(6) in (3+2x+x^(2))^(6).

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