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If f(x)=(1)/(x^(2)), show that f(x)-f(x+...

If `f(x)=(1)/(x^(2))`, show that `f(x)-f(x+1)=(2m-1)/(x^(2)(x+1)^(2))`, hence find the the sum of first n terms of the series `(3)/(1^(2)*2^(2))+(5)/(2^(2)*3^(2))+(7)/(3^(3)*4^(2))+....`

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The correct Answer is:
`(n(n+2))/((n+1)^(2))`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. The sum of first p terms of an A.P. is zero. Show that the sum of a n...

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  2. If a(1),a(2),...a(k) are in A.P. then the equation (S(m))/(S(n))=(m^...

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  3. If f(x)=(1)/(x^(2)), show that f(x)-f(x+1)=(2m-1)/(x^(2)(x+1)^(2)), he...

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  4. Let t(p) be the p th term of an A.P. if its n th tem is zero, show tha...

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  5. Let a,b,c,d, be four quantities such that a+c=2 b and ab+cd+ad=3bc(b n...

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  6. Does there exist a geometric progression containing 27, 8 and 12 as th...

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  7. If a=2 and e=18 , then find three numbers b,c,d betweem a and e such t...

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  8. Prove that any sequence of numbers a(1),a(2),...a(n) satisfying the co...

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  9. If (a-bx)/(a+bx)=(b-cx)/(b+cx)=(c-dx)/(c+dx) show that a,b,c , d are i...

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  10. Prove that 1+(1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+...+ to n terms =(n...

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  11. Show that in A.P. the sum of two terms equidistant from the begining a...

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  12. If there be m quantities in a G.P. whose common ratio is r and S(m)den...

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  13. If a,b,c are in G.P. are log(c) a , log (b) c, log(a) b are in A.P. , ...

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  14. Find the sum to n terms of the following series. 5+555+55555+...

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  15. If x in RR, solve the inequation (5x+8)/(4-x) lt2

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  16. The population of a twon at the beginning of a year is N and the figur...

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  17. Examine the validity of the following statement: If a and b ar odd i...

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  18. Show that the total number of permutations of n diferent things not mo...

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  19. A and B stand in a line with 10 other people. In how many of the perm...

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  20. Find the number of permutations of the letters x,x,x,y,y,y,z,w taken 5...

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