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If |x|<1 and |y|<1, find the sum to infi...

If |x|<1 and |y|<1, find the sum to infinity of the series : `(x+y)+(x^2+x y+y^2)+(x^3+x^2y+x y^2+y^3)+` .......

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. 150 workers were engaged to finish a job in a certain number of days. ...

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  2. The height of a plant at a certain date is 1.6 metre. If it increases ...

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  3. If |x|<1 and |y|<1, find the sum to infinity of the series : (x+y)+(x^...

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  4. A manufacturer reckons that the value of a machine, which costs him Rs...

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  5. Prove the following by using the principle of mathematical induction f...

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  6. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n...

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  7. Find the sum of n terms\ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+do...

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  8. Obtain the sum of the series : 1/1.4+1/4.7+1/7.10 + .......... to n t...

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  9. Find the sum of n terms of the series (1)/(1+1^(2)+1^(4))+(2)/(1+2^(2)...

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  10. Show that : (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. ...

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  11. What will Rs 500 amounts to in 10 years after its deposit in a bank wh...

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  12. A man deposited ₹ 10,000 in a bank at the rate of 5% simple interest a...

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  13. If a, b, c are in A.P. then 3^a, 3^b, 3^c are in:

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  14. If the third term of an A.P is 12 and the seventh term is 24, then the...

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  15. If a, b, c, d, e,f are in A.P., then e - c is equal to

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  16. The third term of a GP is 3. What is the product of the first five ter...

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  17. 5th term of a G.P. is 2, then the product of first 9 terms is:

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  18. If the pth , qth , rth , terms of a GP . Are x,y,z respectively prove ...

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  19. The sum of the first n odd number is :

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  20. If the sum of n natural numbers is one sixth of their squares, then n ...

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