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Find the sum of n terms of the series ab...

Find the sum of n terms of the series `ab+(a-1)(b-1)+(a-2)(b-2)+....` if `ab=1/6` and `a+b=1/3`.

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. The sum of four integar in A.P is 24 and their product is 945. Find th...

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  2. Find the sum of the series 1.n+2(n-1)+3(n-2)+.....n.1.

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  3. Find the sum of n terms of the series ab+(a-1)(b-1)+(a-2)(b-2)+.... if...

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  4. Insert 6 no. between 3 and 24 such that the resulting sequence is an ...

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  5. Between two no. whose sum is 13/6, an even no. of A.M's are inserted ....

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  6. Which term of the G.P. 2,8,32,.... upto n terms is 131072 ?

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  7. Find the least value of n for which 1+3+3^2+....+3^(n-1) gt 1000.

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  8. If p^th ,q^th and r^th terms of a G.P. be a, b, c(a,b,c>0) , prove tha...

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  9. Find the sum of first n terms and the sum of first 5 terms of the geom...

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  10. How many terms of the G.P 3,3/2,3/4 ...... are needed to give the sum ...

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  11. If a1,a2,a3(a1 gt0) are in G.P with common ratio r, then the value of...

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  12. The sum of first three terms of a G.P is 13/12 and their products is -...

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  13. Find the sum of the sequence 7,77,777,7777,......to n terms.

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

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  15. 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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  16. 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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  17. 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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  18. Find the sum of the series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1...

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

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  20. 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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