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The sum (3 xx 1^(3))/(1^(2)) + (5 xx (1^...

The sum `(3 xx 1^(3))/(1^(2)) + (5 xx (1^(3) + 2^(3)))/(1^(2) + 2^(2)) + (7 xx (1^(3) + 2^(3) + 3^(3)))/(1^(2) +2^(2) + 3^(2))...` upto 10th term is

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Sum of first 20 terms of 3/1^2 + 5/(1^2 + 2^2) + 7/(1^2 + 2^2 + 3^2) +... upto 20 terms is :

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Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2)+2^(2))/(1^(3)+2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

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ALLEN-SEQUENCE AND PROGRESSION-Exercise (JM)
  1. If m is the A.M of two distict real numbers l and n (l, n gt 1)and G1,...

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  2. If the 2nd , 5th and 9th terms of a non-constant A.P. are in G.P.,...

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  3. If the sum of the first ten terms of the series (1(3)/(5))^(2)+(2(2)/(...

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  4. If, for a positive integer n , the quadratic equation, x(x+1)+(x-1)(x+...

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  5. For any three positve real numbers a,b and c, 9(25a ^+b^2)+25(c^2-3ac)...

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  6. Let a,b, c in R. " If " f(x)=ax^(2)+bx+c is such that a+B+c=3 and f(x+...

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  7. Let a1,a2,a3…., a49 be in A.P . Such that underset(k=0)overset(12)Sig...

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  8. Let A be the sum of the first 20 terms and B be the sum of the first ...

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  9. If a,b and c be three distinct real numbers in G.P and a+b+c=xb, then ...

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  10. Let a1, a2,...,a30 be an AP, S=sum(i=1)^(30)ai and T=sum(i=1)^(15)a(2i...

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  11. Find sun of first 15 term of series 1+6+(9(1^2+2^2+3^2))/(7)+(12(1^2+...

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  12. If x and y are positive real numbers and m, n are any positive integ...

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  13. If sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, a...

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  14. The sum of all natural numbers ‘n’ such that 100ltnlt200and H.C.F(91,...

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  15. If a ,b ,a n dc are in G.P., then the equations a x^2+2b x+c=0a n ddx^...

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  16. Let the sum of the first n terms of a non-constant A.P., a(1), a(2), a...

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  17. The sum (3 xx 1^(3))/(1^(2)) + (5 xx (1^(3) + 2^(3)))/(1^(2) + 2^(2)) ...

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  18. Let numbers a(1),a(2)…a(16) are in AP and a(1)+a(4)+a(7)+a(10)+a(13)+a...

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  19. If alpha and beta are the roots of the equation 375 x^(2) - 25x - 2 = ...

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  20. If alpha, beta and gamma are three consecutive terms of a non-consta...

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