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Show that 1+(x)/(2)+(x(x-1))/(2.4)+(x(...

Show that
`1+(x)/(2)+(x(x-1))/(2.4)+(x(x-1)(x-2))/(2.4.6)+....`
`=1+(x)/(3)+(x(x+1))/(3.6)+(x(x+1)(x+2))/(3.6.9)+....`

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If (5)/(x-1)+(1)/(y-2)=2,(6)/(x-1)+(-3)/(y-2)=1 then x=……….

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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - 1.3 (Level - 1)
  1. Find the coefficient of x^(3) in the expansion of ((1+3x^(2))^((3)/(2)...

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  2. If |x| is so small that x^(2) and higher powers of x may be neglected ...

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  3. By neglecting x^(4) and higher powers of x, find an approximate value ...

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  4. Expand : 3sqrt(3) in ascending powers of (1)/(3)

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  5. Prove that : Expand 5sqrt(5) in increasing powers of (4)/(5).

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  6. If b is small compared to 'a' show that (c )/((a-b)^(2)) -(c )/((a+b)...

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  7. If 'c' is small in comparison with l then ((l)/(l+c))^(1//2) + ((l)/(l...

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  8. Find the values of the following correct to five decimals. (1)/(roo...

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  9. Find the values of the following correct to five decimals. sqrt(3....

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  10. Find the values of the following correct to five decimals. sqrt(1.0...

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  11. Find the sum of the infinite series 1+(1)/(3)+(1.3)/(3.6)+(1.3.5)/(3...

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  12. Find the sum of the infinite series 1-(4)/(5)+(4.7)/(5.10)-(4.7.10)/...

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  13. Find the sum of the infinite series (3)/(4)+(3.5)/(4.8)+(3.5.7)/(4.8...

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  14. Find the sum of the infinite series (3)/(4.8)-(3.5)/(4.8.12)+(3.5.7)...

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  15. If x=(3)/(16)(3)+(3.7)/(16.32)(3)^(2)+(3.7.11)/(16.32.48)(3)^(3) +… th...

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  16. If t=(4)/(5)+(4.6)/(5.10)+(4.6.8)/(5.10.15)+………oo then prove that 9t=1...

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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)+.... then prove ...

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  18. If x=(5)/((2!).3)+(5.7)/((3!).3^(2))+(5.7.9)/((4!).3^(3))+…. then fi...

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  19. Find the sum of the infinite series (7)/(5)(1+(1)/(10^(2))+(1.3)/(1...

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  20. Show that 1+(x)/(2)+(x(x-1))/(2.4)+(x(x-1)(x-2))/(2.4.6)+.... =1+(...

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