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If sum of first n terms of an AP (having...

If sum of first n terms of an AP (having positive terms) is given by `S_n=(1+2T_n)(1-T_n)` , where `T_n` is the nth term of series , and `T_2^2=(sqrta-sqrtb)/4 (a,b in N)` . Then (a+b) is ____

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Sum of the first n terms of an A.P. having positive terms is given by S_n=(1+2T_n)(1-T_n) (where T_n is the nth term of the series). The value of T_2^2 is (A) (sqrt(2)+1)/(2sqrt(2)) (B) (sqrt(2)-1)/(2sqrt(2)) (C) 1/(2sqrt(2)) (D) none of these

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VMC MODULES ENGLISH-SEQUENCE AND SERIES -LEVEL-2
  1. A computer solved several problems in succession. The time it took to ...

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  2. If a(1),a(2),a(3)(a(1)gt0) are three successive terms of a GP with com...

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  3. Let Sn=1/1^2 + 1/2^2 + 1/3^2 +….. + 1/n^2 and Tn=2 -1/n , then :

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  4. The sum of the series 1/(1*3)+2/(1*3*5)+3/(1*3*5*7)+… is equal to :

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  5. If in a triangleABC , cos (A-C) cos B + cos 2 B =0 , then which of t...

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  6. Let a denotes the number of non-negative values of p for which the equ...

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  7. The series of natural numbers is divided into groups:(1);(2,3,4);(5,6,...

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  8. If the pth, th, rth terms of a G.P. are x, y, z respectively, prove th...

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  9. The sum of a GP, with common ratio 3 is 364 and last term is 243, then...

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  10. Let a1,a2 , …, a10 be in AP and h1,h2,,,, h10 be in HP. If a1=h1=...

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  11. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

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  12. If a,x and b are in AP, a,y and b are in GP and a,z and b are in...

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  13. Find the sum to n terms of the series :1/(1xx2)+1/(2xx3)+1/(3xx4)+dotd...

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  14. If A1,A2,G1,G2 and H1,H2 are AM’s, GM’s and HM’s between two numbers, ...

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  15. For an increasing A.P. a1, a2, an ifa1=a2+a3+a5=-12 and a1a3a5=80 , t...

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  16. If a!= 1 and In a^2 + (In a^2)^2 + (In a^2)^3 + ... = 3 (ln a + (lna)^...

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  17. 1/(2.4) +(1.3)/(2.4.6)+(1.3.5)/(2.4.6.8)+.............oo is equal to

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  18. The sum sum(n=1)^oo (n/(n^4+4)) is equal to p/q then q-p is

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  19. If sum of first n terms of an AP (having positive terms) is given by S...

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  20. If 1/2,1/alpha1 , 1/alpha2 , ….., 1/alpha20 , 1/6 are in A.P. and 1,be...

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