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If x=1+a+a^2+a^3+......infty and y=1+b+b...

If `x=1+a+a^2+a^3+......infty` and `y=1+b+b^2+b^3+......infty` show that `1+ab+a^2b^2+a^3b^3+....infty=(xy)/(x+y-1)` where 0 lt alt1 and 0ltblt1.

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Find the sum of the sequence 7,77,777,7777,......to n terms.

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  2. Find the natural no. a for which sum (k=1)^nf(a+k)=16(2^n-1) where the...

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  3. If x=1+a+a^2+a^3+......infty and y=1+b+b^2+b^3+......infty show that 1...

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  4. If 1/1^2+1/2^2+1/3^2+.... upto infty=pi^2/6 , then, find 1/1^2+1/3^2+1...

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  5. If 1/1^2+1/2^2+1/3^2+.... upto infty=pi^2/6 , then, find 1-1/2^2+1/3^2...

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  6. Find the sum of the series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1...

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  7. Find the sum of series 4-9x+16x^2-25x^3+36x^4-49x^5+..... to infinite...

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  8. If a,b,c be in H.P prove that (1/a+1/b-1/c)(1/b+1/c-1/a)=4/(ac)-3/b^2

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  9. If a,b,c are in H.P. show that a/(b+c),b/(c+a),c/(a+b) are also in H.P...

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  10. Prove that the sum of n arithmatic means between two numbers is n time...

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  11. Find the sum to n terms of the series: 5+11+19+29+41.....

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  12. Find the sum of n terms of the series 3+7+14+24+37+.....

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  13. Find the sum of series 3+8+22+72+266+1036+....

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  14. Prove that sum(n=1)^infty n/(4n^4+1) equals to 1/4.

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  15. Prove that sum(n=1)^infty n/(4n^4+1) equals to 1/4.

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  16. Show that the sum of sum(n=1)^infty n/(n^4+4) equals to 3/8

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  17. Show that the sum of sum(n=1)^infty n/(n^4+4) equals to 3/8

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  18. Find the sum of first n terms of the series 3/1^2+5/(1^2+2^2)+7/(1^2+2...

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  19. Find the sum of the series 1/(1.2.3.4)+1/(2.3.4.5)+1/(3.4.5.6)+..........

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  20. Find the sum of 2.3+3.4+4.5+......to n terms.

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