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Find the sum of the infinitely decreasin...

Find the sum of the infinitely decreasing G.P. whose third term, three times the product of the first and fourth term and second term form an A.P. in the indicated order, with common difference equal to `1/8`.

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FIITJEE-PROGRESSION & SERIES -ASSIGNMENT PROBLEMS (SUBJECTIVE) LEVEL-II
  1. The series of natural numbers is divided into groups (1),(2,3,4) : ...

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  2. Find the value of 2551 S where S = sum(k=1)^(50) k/(k^(4)+k^(2)+1)

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  3. If an=3/4-(3/4)^2+(3/4)^3+...(-1)^(n-1)(3/4)^n and bn=1-an, then find ...

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  4. If S=a+b+c then prove that (S)/(S-a)+(S)/(S-b)+(S)/(S-c) gt (9)/(2) wh...

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  5. Sum to n terms of the series 1+(1+x)+(1+x+x^2)+(1+x+x^2+x^3)+...

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  6. (1^4)/1.3+(2^4)/3.5+(3^4)/5.7+......+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5))...

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  7. The sum of the infinite series (1)/(3)+(3)/(3.7)+(5)/(3.7.11)+(7)/(3...

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  8. Find the minimum value of (a+1/a)^(2) +(b+1/b)^(2) where a gt 0, b g...

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  9. If m is negative or positive and greater than 1 , show that 1^(m)+...

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  10. Let a,b,c be three distinct positive real numbers in G.P , then pr...

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  11. The nth term of a series is given by t(n)=(n^(5)+n^(3))/(n^(4)+n^(2)+1...

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  12. If sum(r=1)^n tr=n/8(n+1)(n+2)(n+3), then find sum(r=1)^n1/(tr)dot

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  13. If the terms of A.P. sqrt(a-x),sqrt(x),sqrt(a+x) ……….. Are all integer...

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  14. If the terms of the A.P. sqrt(a-x),sqrt(x),sqrt(a+x) are all in intege...

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  15. Prove that (666 …. "to n digits")^(2) +(888 …. To n digits ) = (444 … ...

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  16. Find the sum of the infinitely decreasing G.P. whose third term, three...

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  17. If the equations ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0 have a commo...

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