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Sum of the series 1-(1)/(2)+1/(2^2)-1/(2...

Sum of the series `1-(1)/(2)+1/(2^2)-1/(2^3)+............oo=.........`

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The correct Answer is:
`2/3`
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KUMAR PRAKASHAN-OBJECTIVE SECTION AS PER NEW PAPER SCHEME -Sequence and Series (Fill in the blanks )
  1. For arithmetic sequence a = 2 and a5 = 14 then d = ........

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  2. For arithmetic sequence a(8) =23 common difference d = 5 then a = .......

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  3. For arithmetic sequence

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  4. For an A.P a = 20 and l = 97 then S(20)= ..........

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  5. If a, b, and c are in A.P then (a + 2b -c) . ( 2b +c-a) . (c+a-b) = .....

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  6. For arithmetic sequence a(1),a(2),a3 ........ If a(1)+a(5)+a(10)+a(15)...

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  7. If 25, x - 6 and x - 12 are in G.P then x = .......... or ......... .

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  8. Third term of G.P. is 3 then product of its first 5 terms is ............

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  9. Eighth term of G.P is 128 and common ratio is r = 2 then product of fi...

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  10. For an G.P. a = 16 and fifth term is 81 then common ratio ........

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  11. How many terms of G.P. 3, 3^2, 3^3, … are needed to give the sum 120?

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  12. For an geometric seq. (5)/2,(5)/(4),(5)/8.......a(n) = ............. .

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  13. A1 and A2 are arithmetic mean between a and b also G1 and G2 are geome...

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  14. For numbers 6 and 24, A - G = ...... .

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  15. 10 is Geometric mean between 5 and x then x = ......... Where x in R^(...

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  16. 12 is arithmetic mean between x and 22 then x = ............

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  17. 10 arithmetic mean between a and b are A(1),A(2),A(3).........A(10) th...

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  18. If sumn = 55 then sumn^2 . = ...............

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  19. sum(r=1)^n(2r+1)=...... .

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  20. Sum of the series 1-(1)/(2)+1/(2^2)-1/(2^3)+............oo=.........

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