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Show that 1 + 1/2.3/5 + (1.3)/(2.4) (3/...

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])`

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Verified by Experts

The correct Answer is:
`sqrt(5/2)`
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Show that 1 + 2/3.1/2 + (2.5)/(3.6) (1/2)^2 + (2.5.8)/(3.6.9) (1/2)^3 + ….. = root(3)4

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

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

1+(1)/(2). (3)/(5) + (1.3)/(2.4) . (9)/(25)+(1.3.5)/(2.4.6).(27)/(125)+…...oo=

1+(1)/(2!)+(1.3)/(4!)+(1.3.5)/(6!)+...=

(3)1/2+(5)3/4

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

AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. Find the value of (627)^(1//4) correct to 4 decimals places

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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