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(1^4)/1.3+(2^4)/3.5+(3^4)/5.7+......+n^4...

`(1^4)/1.3+(2^4)/3.5+(3^4)/5.7+......+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5))/48+n/(16(2n+1)`

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

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

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

Find the sum (1^(4))/(1xx3)+(2^(4))/(3xx5)+(3^(4))/(5xx7)+......+(n^(4))/((2n-1)(2n+1))

1.4+2.5+.......+n(n+3)=

Using the principle of mathematical induction prove that (1)/(1.2.3)+(1)/(2.3.4)+(1)/(3.4.5)+...+(1)/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2) for all n in N

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(1.2.3)+(1)/(2.3.4)+(1)/(3.4.5)+...+(1)/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2))

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+...+(1)/((3n-1)(3n+2))=(n)/((6n+4))=(n)/((6n+4))

1^(3)+2^(3)+3^(3)+.....+n^(3)=(n(n+1)^(2))/(4), n in N

1.2.3+2.3.4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

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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