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Find the sum as directed.1+4x+8x^2+13x^3...

Find the sum as directed.`1+4x+8x^2+13x^3+19x^4+...` (to infinity) Assuming that the series has a sum for `|x|lt1`.

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MBD PUBLICATION-SEQUENCES AND SERIES-QUESTION BANK
  1. Find the sum as directed.1+(1+x)y+(1+x+x^2)y^2+... (to infinity)

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  2. Find the sum as directed.1+3/5+7/25+15/125+31/625+... (to infinity)

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  3. Find the sum as directed.1+4x+8x^2+13x^3+19x^4+... (to infinity) Assum...

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  4. Find the sum as directed.3.2+5.2^2+7.2^3+.... (first n terms)

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  5. Find the sum of the infinite series. 1/(1.2)+1/(2.3)+1/(3.4)+...

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  6. Find the sum of the infinite series.1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+...

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  7. Find the sum of the infinite series.1/(2.5.8)+1/(5.8.11)+1/(8.11.14)+....

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  8. Find the sum of the infinite series.3/(1^(2).2^(2))+5/(2^(2).3^(2))+7/...

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  9. Find the sum of the infinite series. 1/(1.5)+1/(3.7)+1/(5.9)+...

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  10. Find Sn for the series. 1.2 + 2.3 + 3.4 +…

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  11. Find Sn for the series. 1.2.3 + 2.3.4 + 3.4.5 +….

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  12. Find Sn for the series. 2.5.8 + 5.8.11 + 8.11.14 +...

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  13. Find Sn for the series. 1.2.3.4 + 2.3.4.5 + 3.4.5.6 +…

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  14. Find Sn for the series. 1.5 + 2.6 + 3.7 + …..

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  15. Find Sn for the series. 2.3 + 3.6 + 4.11 + ….

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  16. Find Sn for the series. 1.3^2+2.5^2+3.7^2+...

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  17. Find the sum of first n terms of the series, 5+6+8+12+20+…

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  18. Find the sum of first n terms of the series, 4+5+8+13+20+…

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  19. Find the sum of the product of 1,2,3….20 taken two at a time.

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  20. Do the same for 1, 3, 5, 7,…..19.

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