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

If f(x)=`1/x^2`,show that `f(x)-f(x+1)=(2x+1)/(x^2(x+1)^2)`and hence again show that `3/(1^2. 2^2)+5/(2^2 .3^2)+7/(3^2 .4^2)+...+(2n+1)/(n^2(n+1)^2)=(n^2+2n)/((n+1)^2)`

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 9-EXERCISE
  1. Find the probability of 53 Sunday in a Leap year ?

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  2. Show that the mean deviation with respect to Arithmetic mean is zero

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

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  4. If acosphi=b costheta,show that a tantheta+b tanphi=(a+b)tan((theta+ph...

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  5. Show that tan20^@tan40^@tan80^@=sqrt3

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  6. Prove the following by the method of mathematical induction. :n^3+(n+1...

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  7. If the sum of 1+2r+3r^2+4r^3+...oo9/16,find the value of r.

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  8. In how many ways can the crew of an 8-oared boat be arranged if 2 of t...

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  9. Express(sqrt3-i)/(1-sqrt3i)in modulus amplitude form

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  10. In /\XYZthe equation of the perpendicularbisector of XY and XZ arc x-y...

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  11. Find the co-ordinate of the image of the point (-3, -1), with respect ...

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  12. Show that the circle with the portion of the line 3x + 4y = 12 interce...

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  13. Find the equation to the locus of a point whose distance from YZ plane...

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  14. Evaluate the following limits :lim(xrarr0)(xtan2x-2xtanx)/((1-cos2x)^2...

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  15. If f(x)=|x-1|1+x^2.Is f'(x) exist?examine it.

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  16. Using contrapositive method show tha the compund statement .is true or...

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  17. Show that sqrt3is irrational. (Use the method of contradiction).

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  18. If the letters of the word PROBABILITY be arranged at random, find the...

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  19. AM and SD of 7- observations are 8 and 4. If 5.of the 7 observations a...

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  20. Find the maximum and minimum value of 5costheta+12sintheta+12

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