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Let x=1+a +a^(2) +….. And y= 1 + b + b^(...

Let `x=1+a +a^(2) +`….. And `y= 1 + b + b^(2)+`…… where `|a| lt 1` and `|b| lt 1`. Prove that: `1+ ab + a^(2)b^(2) +…… =(xy)/(x+y-1)`.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Find a rational number of the following which will have as its expansi...

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  2. Find a rational number of the following which will have as its expansi...

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  3. Let x=1+a +a^(2) +….. And y= 1 + b + b^(2)+…… where |a| lt 1 and |b| l...

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  4. One side of a equilateral triangle is 24 cm. The mid-points of its sid...

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  5. Find the sum to n terms of the following series : 1+3/2+5/2^2+7/2^3+...

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  6. Find the sum to n terms of the following series : 1+2/3 +3/3^2+4/3^3...

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  7. Find the sum to n terms of the following series : 3+5xx 1/4+7xx1/4^2...

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  8. Find the sum to n terms of the following series : 1+2x+ 3x^2+4x^3+ ....

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  9. Find the sum to n terms of the following series : 1+ 3x+ 5x^2+7x^3+ ...

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  10. Find the sum to n terms of the following series : 1+4x+7x^2+10x^3+ ....

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  11. Find the sum to infinity of the following series : 2+3/2+1+5/8+........

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  12. Find the sum to infinity of the following series : 1+2/3+ 3/3^2+4/3^...

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  13. Find the sum to infinity of the following series : 1-3/2+5/4-7/8+ .....

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  14. Find the sum to infinity of the following series : 1-2/3 + 3/3^2-4/3...

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  15. If the sum to infinity of the series 3+5r+7r^2+………is 44/9. Find r.

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  16. If the sum to infinity of the series : 1-(1+d)xx1/3+(1+2d)xx1/9 -(1+3...

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  17. Sum to n terms the series : 2+5x + 8x^2+11x^3+........., |x| < 1.

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  18. Prove that : 2^(1/4)xx4^(1/8)xx8^(1/16)xx16^(1/32)xx ....... → oo =2.

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  19. Find the sum of the following series : 2^2+4^2+6^2 + .... to n terms...

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  20. Find the sum of the following series : 1^3+3^3+5^3+ .... to n terms ...

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