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Let Sn denote the sum of first n terms o...

Let `S_n` denote the sum of first n terms of the sequence 1,5,14,30,55,..... then prove that `S_n-S_(n-1)=sumn^2`.

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Find 1+2^2x+3^2x^2+4^2x^3+.... to infty absx lt 1.

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  2. Find the sum of 1st n terms of the sequence 3,6,15,42,123,...

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  3. Let Sn denote the sum of first n terms of the sequence 1,5,14,30,55,.....

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  4. Finds the sum of first n terms of the series 3/(1^2xx2^2)+5/(2^2xx3^2)...

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  5. How many terms of the series 54+51+48+45+ ... must be taken to make 51...

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  6. If (b+c),(c+a),(a+b) are in H.P. show that a^2 ,b^2 , c^2 are in A.P.

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  7. 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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  8. If 0 < theta < pi/2 then find the least value of tantheta+cottheta

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  9. If x and y are positive quantities whose sum is 4, show that (x+1/x)^2...

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  10. If a,b,c gt 0 show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)le(a+b+c)/2.

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  11. Show that a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)ge6abc.

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  12. If m, n are positive quantities, prove that ((mn+1)/(m+1))^(m+1)gen^m.

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  13. Prove that ((bc+ac+ab)/(a+b+c))^(a+b+c)ge(b)^a(c)^b(a)^c [where a,b,c ...

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  14. If log2,log(2^n-1) and log(2^n+3) are in A.P. then n =

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  15. If the ratiio of the sum of n terms ofd two AP's is (3n+1):(2n+3) then...

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  16. If a1,a2,a3,.......an are in AP where a1 gt 0foralli then the value of...

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  17. Given p no. of A.P. each of which consists of an n terms. If their fir...

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  18. Answer the following question based on above passage: The coefficient...

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  19. If a,b,c ,d and p are distinct real number such that (a^2+b^2+c^2)p^2-...

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  20. Suppose a,b,c are in A.P and a^2,b^2,c^2 are in G.P. If a lt b lt c an...

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