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(1)/(2 !)+(2)/(3 !)+(3)/(4 !)+.. .. to n...

 `(1)/(2 !)+(2)/(3 !)+(3)/(4 !)+.. .. to n terms =`

A

`1-(1)/((n+1) !)`

B

`1+(1)/((n+1) !)`

C

` 1-(1)/(n !)`

D

`1+(1)/(n !)`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. 1+(3)/(2)+(5)/(2^(2))+(7)/(2^(3))+.. .. to infty=

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  2. Sum to n terms of the series3+15+35+63+.. ..

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  3. (1)/(2 !)+(2)/(3 !)+(3)/(4 !)+.. .. to n terms =

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  4. Sum of 10 terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1+2...

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  5. If the sum of n terms of the series : (1)/( 1^(3)) +( 1+2)/( 1^(3) +...

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  6. Sum of 25 terms of the series 1 . 3+2 . 5+3 . 7+.., is

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  7. If the natural numbers are divided into the groups (1),(2,3),(4,5,6),(...

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  8. If (sum n^(3))(sum n)=(sum n^(2))^(2), then

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  9. 4^(3)+5^(3)+6^(3)+.. .+10^(3)=

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  10. 3+5+7+ …..to n^(th) term is

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  11. ((1)/(2) . (2)/(2))/(1^(3))+((2)/(3) . (3)/(2))/(1^(3)+2^(3)) +((3)/(2...

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  12. The 10^(th ) term of the series 3+13+29+51+79+.. ..

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  13. Sum to 30 terms of 3+4+8+9+13+14+18+19+.. is

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  14. The greatest positive integer, which divides (n+1)(n+2)(n+3)(n+4) for ...

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  15. The sum of cubes of three successive natural numbers is divisible by

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  16. Product of 4 consecutive natural numbers is divisible by

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  17. 49^(n)+16 n-1 is divisible by

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  18. If n is a positive integer, then n^(3)+2n is divisible

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  19. If n in N then 3 . 5^(2 n+1)+2^(3 n+1) is divisible by

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  20. If n is a +ve integer, 4^(n)-3 n-1 is divisible by

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