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Prove by mathematical induction that1/1....

Prove by mathematical induction that`1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n+1))`=`n/(2n+1),(n in N)`

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Prove by mathematical induction. 1/1.3+1/3.5+1/5.7+....+1/((2n-1)(2n+1))=n/(2n+1)

Prove by induction that (1)/(1*3)+(1)/(3*5)+(1)/(5*7)+ . . .+(1)/((2n-1)(2n+1))=(n)/(2n+1)(ninNN) .

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 by mathematical induction that, 1^(2)-2^(2)+3^(2)-4^(2)+ . . .. +(-1)^(n-1)*n^(2)=(-1)^(n-1)*(n(n+1))/(2),ninNN .

For all ninNN , prove by principle of mathematical induction that, 1*2+2*3+3*4+ . . . +n(n+1)=(1)/(3)n(n+1)(n+2) .

Prove that by using the principle of mathematical induction for all n in N : 1.3+3.5+5.7+....+(2n-1)(2n+1)= (n(4n^(2)+6n-1))/(3)

Prove the following by the principle of mathematical induction: \ 1. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove by mathematical induction 1^(2)+2^(2)+3^(2)+.....+(n+1)^(2)=((n+1)(n+2)(n+3))/(6)

Prove by. mathematical induction : 1.2+2.2^2+3.2^3+...+n.2^n=(n-1)2^(n+1)+2,n in N

For all ninNN , prove by principle of mathematical induction that, (1)/(1*2)+(1)/(2*3)+(1)/(3*4)+ . . .+(1)/(n(n+1))=(n)/(n+1) .

UNITED BOOK HOUSE-TECHNO INDIA GROUP ACADEMIA,SOUTH KOLKATA.-EXERCISE
  1. In any /\ABC,prove that sin(B-C)/(sin(B+C))=(b^2-c^2)/(a^2)

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  2. Prove that,cosx/(1-sinx)=tan(pi/4+x/2)

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  3. Prove by mathematical induction that1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n...

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  4. If x+iy=2/(3+costheta+isintheta),show that 2x^2+2y^2=3x-1

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  5. find the co-efficient of (2r+4)th and (r-2)th terms in the expansion o...

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  6. If p, q, r are in G.P and the equation px^2+2qx+r=0 and dx^2+2ex+f=0 h...

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  7. Show that the points (a,0),(0,b)and (3a,-2b)are collinear.Also find th...

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  8. Find the distance between the parallel lines 4x-3y+5=0 and 4x-3y+7=0.

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  9. Find the equation of a circle through origin which cuts of intercepts ...

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  10. Find the value of the limit lim(nrarroo)(1^2+2^2+...+n^2)/n^3

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  11. If y=sqrt((1-x)/(1+x)),prove that (1-x^2)dy/dx+y=0

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  12. If x^2is an odd number then x is also odd number,justify the validity ...

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  13. If x and y are odd integers, then xy is also an odd integer r examine ...

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  14. In single throw of two dice,the probality of obtaning 'a total of 8' i...

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  15. Find S.D from the following data:

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  16. Solve :sqrt3cosx-sinx=1

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  17. Prove that, cos20^@cos40^@cos60^@cos80^@=1/16

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  18. Exhibit graphically the solution sets of the following system of linea...

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  19. Solve :3x^2+8ix+3=0

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  20. Find the sum of n terms of the series 1/2.5+1/5.8+1/8.11…to n terms.

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