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For a positive integer n let a(n)=1+1/2+...

For a positive integer n let `a(n)=1+1/2+1/3+1/4+.......+1/((2^n)-1)` then

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Let Tr be the rth term of an A.P., for r=1,2,3,..... If for some pos...

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  2. Let An = (3/4) -(3/4)^2 + (3/4)^3 +.....+(-1)^(n - 1) (3/4)^n , Bn = 1...

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  3. For a positive integer n let a(n)=1+1/2+1/3+1/4+.......+1/((2^n)-1) th...

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  4. If x >1,y >1,a n dz >1 are in G.P., then 1/(1+lnx),1/(1+l ny)a n d1/(1...

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  5. Compute the 100th term of HP if the 10th and 20th term of HP are 20 an...

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  6. Find the 6th and nth term of the GP 2, 6, 18, 54,.....

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  7. If a,b,c are in AP and a^2,b^2,c^2 are in HP, then

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  8. Let a ,b be positive real numbers. If a, A1, A2, b be are in arithmeti...

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  9. The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...

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  10. If a^2+b^2,a b+b c and b^2+c^2 are in G.P., then a ,b ,c are in a. A.P...

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  11. If y^2=x za n da^x=b^y=c^z , then prove that (log)6a=(log)c bdot

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  12. The geometric mean between -9 and -16 is a.12 b. -12 c. -13 d. none of...

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  13. The value of 0.568 x 4.9 =?

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  14. If (1+x)(1+x^2)(1+x^4)....(1+x^128)=sum(r=0)^nx^r then n is

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  15. The number of terms common between the series 1+ 2 + 4 + 8..... to 100...

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  16. Express the given complex number in (a+ib) form: (5-2i)^2

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  17. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

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  18. If (a-b), (b-c), (c-a) are in GP then prove that (a+b+c)^2 =3(ab+bc+ca...

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  19. Given that x+y+z=15 when a ,x ,y ,z ,b are in A.P. and 1/x+1/y+1/z=5/3...

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  20. Let a1,a2,a3…… ,an be in G.P such that 3a1+7a2 +3a3-4a5=0 Then find c...

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