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If the sequence `a_1, a_2, a_3,....... a_n ,dot` forms an A.P., then prove that `a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)`

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RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If a, b, c are in A.P. and b-a, c-b, a are in G.P. then a:b:c=?

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  2. Evaluate: int(x+1)/(x(1+xe^x)^2)dx

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  3. If the sequence a1, a2, a3,....... an ,dot forms an A.P., then prove ...

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  4. If int0^a(dx)/(sqrt(x+a)+sqrt(x))=int0^(pi/8)(2tantheta)/(sin2theta)d ...

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  5. The sum of the first three terms of an arithmetic progression is 9 and...

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  6. int("sin"2"x")/(sin5x .sin3x)dx a.1/3ln|sin3x|+1/5ln|sin5x|+c b. ...

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  7. A postman delivered daily for 42 days 4 more latters each day than on ...

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  8. If int0^1tan^(-1)xdx=alpha,t h e nint0^(pi/4)tan^(-1)((2cos^2theta)/(...

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  9. If in a triangle A B C , right angle at B ,s-a=3a n ds-c=2, then a=2,c...

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  10. The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,...

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  11. In a triangle A B C , right angled at B , the inradius is (A B+B C-A C...

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  12. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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  13. Vectors vec a\ a n d\ vec b are inclined at angel theta=120^0 . If |...

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  14. Evaluate the following inte^x(1-cot x+cot^2x)dx

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  15. If for a real number y ,[y] is the greatest integral function less, th...

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  16. int(1)/(sqrt(2x^(2)+3x-2))dx

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  17. If the value of the integral int1^2e^(x^2)dx is alpha, then the value ...

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  18. Find the particular solution of the differential equation (dy)/(dx)= (...

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  19. If int(2x+3)/(x^2-5x+6)dx=9ln|x-3|-7ln|x-2|+A ,t h e nA is 5ln(x-2)+...

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  20. Normals are drawn from the point P with slopes m(1),m(2)andm(3) to tha...

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