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Sum the series to infinity : sqrt(3) ...

Sum the series to infinity :
`sqrt(3) + (1)/(sqrt(3))+ (1)/(3sqrt(3))+...`

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The correct Answer is:
`(3 sqrt(3))/(2)`
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ICSE-SEQUENCE AND SERIES -EXERCISE 14 (f)
  1. Sum the series to infinity : 16 ,-8,4 , .....

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  2. Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2))...

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  3. Sum the series to infinity : sqrt(3) + (1)/(sqrt(3))+ (1)/(3sqrt(3)...

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  4. Find the sum of a geometric series in which a=16 , r=(1)/(4) ,l = (1)...

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  5. Find the sum of the series 81 -27 +9 - ...... -(1)/(27) .

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  6. The first three terms of a G.P. are x x +3, x+ 9. Find the value of x ...

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  7. Of how many terms is ,(55)/(72) the sum of the series (2)/(9) -(1)/(3...

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  8. The second term of a G.P. is 2 and the sum of infinite terms is 8. Fin...

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  9. Find the value of 0.23434343434..... regarding it as a geometric serie...

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  10. Evaluate : (a) 0.9bar7 (b) 0.2345

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  11. Find a rational number which when expressed as a decimal will have 1.2...

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  12. If a+b+.... + l is a G.P., prove that its sum is (bl-a^(2))/(b-a) .

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  13. The nth term of a geometrical progression is (2^(2n-1))/(3) for all va...

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  14. A geometrical progression of positive terms and an arithmetical progre...

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  15. In a geometric progression, the third term exceeds the second by 6 and...

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  16. In an infinite geometric progression, the sum of first two terms is 6 ...

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  17. Three numbers are in A.P. and their sum is 15. If 1,4 and 19 be added ...

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  18. Calculate the least number of terms of the geometric progression 5 + 1...

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  19. If S is the sum, P the product and R the sum of the reciprocals of n t...

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  20. Find the sum of the first n terms of the series: 0.2 + 0.22 + 0.222+...

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