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If x=1 +a + a^2+…. to oo, where |a| lt1 ...

If `x=1 +a + a^2+….` to `oo`, where `|a| lt1` and `y=1+b+b^2+…` to `oo` , where `|b|lt1`, prove that `1+ab+a^2b^2+…` to `oo=((xy)/(x+y-1))`

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A N EXCEL PUBLICATION-SEQUENCES AND SERIES-QUESTION BANK
  1. The first term of a G.P is 1. The sum of the third and fifth terms is ...

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  2. Find sum of 5 + 55 + 555 + ... to n terms.

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  3. If x=1 +a + a^2+…. to oo, where |a| lt1 and y=1+b+b^2+… to oo , where ...

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  4. A square is drawn by joining the mid points of the sides of a square. ...

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  5. Find the 20^(th) and n^(th) terms of the G.P. 5/2,5/4,5/8,…

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  6. Find the 12^(th) term of a G.P. whose 8^(th) term is 192 and the commo...

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  7. The 5^th, 8^th and 11^th terms of a GP are p, q and s respectively. Pr...

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  8. The 4^(th) term of a G.P. is square of its second term and the first t...

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  9. Which term of the following sequences 2,2sqrt2,4…is 128?

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  10. Which term of the following sequences sqrt3,3,3sqrt3,...is 729?

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  11. Which term of the following sequences 1/3,1/9,1/27,...is1/19683?

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  12. Find the sum to 20 terms of 0.15,0.015,0.0015,..

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  13. For what value of x, the numbers -2/7,x.-7/2 are in G.P ?

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  14. Find the sum to n terms of the G.P.sqrt7,sqrt21,3sqrt7…

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  15. Find the sum to n terms of the G.P. 1,-a,a^2,-a^3,...(ane-1)

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  16. Find the sum to n terms of the G.P.x^3,x^5,x^7,…(xne+-1)

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  17. Evaluate underset(K=1)overset11sum(2+3^K)

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  18. The sum of the first three terms of a GP is (39)/(10) and their produc...

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  19. How many terms of the G.P.3,3^2,3^3,… are needed to give the sum 120?

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  20. The sum of first three terms of a G.P. is 16 and the sum of the next ...

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