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If |x| is so small that x^2 and higher p...

If |x| is so small that `x^2` and higher powers of x many be neglected , prove that `((1 + 7x)^(2/3) . (1 - 4x)^(-2))/((4 + 7x)^(1/2)) = 1/2 (1 + 283/24 x)`

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If |x| is so small that x^2 and higher powers of x many be neglected , prove that sqrt(9 - 2x) (3 + (4x)/(5))^(-1) = 1 - 17/45 x

If |x| is so small that x^2 and higher powers of x may be neglected show that ((1 -2/3 x)^(3//2) . (32 + 5x)^(1//5))/((3 - x)^3) = 2/27 (1 + (x)/(32))

If |x| is so small that x^2 and higher powers of x may be neglected show that ((4 - 7x )^(1//2))/((3 + 5x)^3) = 2/27 (1 - 47/8 x)

If |x| is so small that x^2 and higher powers of x may be neglected show that ((4 + 3x)^(1//2))/((3 - 2x)^2) = 2/9 + 41/108 x

If |x| is so small that x^2 and higher powers of x may be neglected show that (sqrt(4 -x )) (3 - x/2)^(-1) = 2/3 (1 +(x)/(24))

If x is so small that x^2 and higher powers of x may be neglected then ((1-3x)^(1//2) (1+x) ^(2//3))/((1-x)^(1//2))

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If |x| is so small that x^2 and higher powers of x may be neglected show that ((8 + 3x)^(2//3))/((2 + 3x)sqrt(4 - 5x)) = 1 - (5x)/(8)

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AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. Find the coefficient of x^12 in ((1+ 3x))/((1 -4x)^4)

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  2. If |x| is so small that x^4 and higher powers of x many be neglected ,...

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  3. If |x| is so small that x^2 and higher powers of x many be neglected ,...

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  4. If |x| is so small that x^2 and higher powers of x many be neglected ,...

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  5. If x is so small that x^2 and higher powers of x many be neglected , s...

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  6. If x is so small that x^2 and higher powers of x many be neglected , s...

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  7. Find the value of (1.02)^(3//2) - (0.98)^(3//2) correct to 6 decimals ...

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  8. Find the value of root(5)(32.16) correct to 4 decimals places

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  9. Find the value of (627)^(1//4) correct to 4 decimals places

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

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  11. Show that 1 + 1/2.3/5 + (1.3)/(2.4) (3/5)^2 + (1.3.5)/(2.4.6) (3/5)^3...

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  12. Sho that 3/6 + (3.5)/(6.9) + (3.5.7)/(6.9.12)+ ……..oo 3 sqrt3 - 4

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

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  14. Show that (4.6)/(5.10) + (4.6.8)/(5.10.15) + (4.6.8.10)/(5.10.15.20) +...

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

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

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

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

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

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