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Show that the square root of 3^((1)/(2))...

Show that the square root of `3^((1)/(2))xx9^((1)/(4))xx27^((1)/(8))xx81^((1)/(16))xx...` to infinity is 3.
[ Note : When we are asked to find the square root of a number, it is presumed that we have to find the principal square root.]
Find the sum of the series `(1)/(2)+(2)/(4)+(3)/(8)+(4)/(10)+...oo` and substitute in (1).]

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ICSE-SEQUENCE AND SERIES -EXERCISE 14 (h)
  1. Find the sum of x+2x^(2)+3x^(3)+4x^(4)+...

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  2. 1^(2)+ 3^(2)x+ 5^(2)x^(2)+ 7^(2)x^(3)+.....

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  3. Show that the square root of 3^((1)/(2))xx9^((1)/(4))xx27^((1)/(8))xx8...

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  4. Find the sum to n terms of the series whose nth term is n (n+2)

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  5. Find the sum to n terms of the series whose nth term is 3n^(2)+2n

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  6. Find the sum to n terms of the series whose nth term is 4n^(3)+6n^(...

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  7. Find the sum of the series 3xx5+ 5xx7+ 7xx9+ .. to n terms

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  8. Find the sum of the series 1^(2)+3^(2)+5^(2)+... to n terms

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  9. Find the sum of the series 2^(2)+4^(2)+6^(2)+... to n terms.

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  10. Find the nth term and the sum to n terms of the series 1.2+ 2.3 +3.4 +...

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  11. Sum up to n terms the series 1.2^(2)+2.3^(2)+ 3.4^(2)+...

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  12. Sum up 1 + (1+2)+(1+ 2+3) +...+(1+2+3+...+ n ).

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  13. The sum to n terms of series 1+(1+1/2+1/(2^2))+(1+1/2+1/(2^2)+1/(2^3))...

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  14. Sum up to n terms the series where nth terms is 2^(n) -1

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  15. The number of terms common between the series 1+2+4+8+ .......to 100 t...

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  16. Sum up 3+5+11 +29 + .... To n terms .

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  17. Sum to n terms the series 7+77+777+....

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  18. Sum to n terms the series 1+3+7+15+31+...

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  19. Find the sum to n terms of the series (1.2.3) + (2.3.4) + (3.4.5) ...

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  20. Find the sum of the series to n terms and to infinity : (1)/(1.3)+ (1)...

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