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In an A.P. if p^(th) term is 1/q and q^(...

In an A.P. if `p^(th)` term is `1/q and q^(th)` term is `1/p` , prove that the sum of first pq terms is `1/2(pq+1)` , where `p ne q`.

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PATHFINDER-SEQUENCES AND SERIES-QUESTION BANK
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  2. The ratio of the sums of m and n terms of an A.P. is m^2 : n^2. Show ...

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  3. If (a^(n+1)+b^(n+1))/(a^n+b^n) is the A.M between a and b then find th...

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  4. If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and ...

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  5. If (a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx) (x+-0) then show a,b,c an...

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  6. Sum to n term .7+.77+.777.......

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  7. The difference between any two consecutive interior angles of a polygo...

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  8. The sum of n term of three A.P are S1,S2,and S3. The frist term of eac...

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  9. If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N ...

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  10. Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/...

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  11. Find the sum of the infinite series 1+(2)/(3)+(3)/(3^2)+(4)/(3^3)+.......

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

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  13. If the sum of n terms of an A.P. is (pn + qn^2) , where p and q are co...

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  14. If the sum of first p terms of an A.P. is equal to the sum of the firs...

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  15. Evaluate sum(k=1)^11(2+3^k)

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  16. If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively...

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  17. If the first and the n^("th") term of a G.P. are a and b, respectivel...

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  18. Find the sum to n terms of each of the series in 1^2 + (1^2 + 2^2...

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  19. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3 , respectiv...

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  20. The p th ,q th and r th terms of an A.P are a,b,c respectively. Show t...

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