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If p^th ,q^th and r^th terms of a G.P. b...

If `p^th` ,`q^th` and `r^th` terms of a G.P. be a, b, c(a,b,c>0) , prove that (q-r) log a +(r-p) logb +(p-q) logic=0.

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Which term of the G.P. 2,8,32,.... upto n terms is 131072 ?

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

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  3. 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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  4. Find the sum of first n terms and the sum of first 5 terms of the geom...

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

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

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

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

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

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  10. 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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  11. 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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  12. 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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  13. Find the sum of the series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1...

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

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  15. 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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  16. 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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  17. Prove that the sum of n arithmatic means between two numbers is n time...

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

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

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

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