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If a1,a2,a3,...,aaare in A.P then show t...

If `a_1,a_2,a3,...,a_a`are in A.P then show that `1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1))=(n-1)/(a_1a_n)`

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If a_1,a_2,a3,...,a_n are in A.P then show that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n)

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n

If a_(1) ge 0 for all t and a_(1), a_(2), a_(3),….,a_(n) are in A.P. then show that, (1)/(a_(1)a_(3)) + (1)/(a_(3)a_(5)) +...+ (1)/(a_(2n-1).a_(2n+1)) = (n)/(a_(1)a_(2n+1))

If a_(1), a_(2), a_(3),…, a_(n) be in A.P. Show that, (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) +….+(1)/(a_(n-1)a_(n)) = (n-1)/(a_(1)a_(n))

If a_(1), a_(2), a_(3), …., a_(n) are in H.P., prove that, a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) +…+ a_(n-1)a_(n) = (n-1)a_(1)a_(n)

If a_1,a_2,.....a_n are in H.P., then the expression a_1a_2 + a_2a_3 + ... + a_(n-1)a_n is equal to

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If a_(1) ge 0 for all t and a_(1), a_(2), a_(3),….,a_(n) are in A.P. then show that, (1)/(sqrt(a_(1))+sqrt(a_(2)))+(1)/(sqrt(a_(2))+sqrt(a_(3)))+ (1)/(sqrt(a_(n-1))+sqrt(a_(n))) = (n-1)/(sqrt(a_(1))+sqrt(a_(n)))

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)

If the coefficients of four consecutive terms in the expansion of (1+x)^n are a_1,a_2,a_3 and a_4 respectively. then prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2a_2/(a_2+a_3).

UNITED BOOK HOUSE-HARE SCHOOL-EXERCISE
  1. If G is the G.M between two positive numbers a and b.show that 1/(G^2-...

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  2. Three positive numbers a,b,c are in A.P prove that 1/(sqrtb+sqrtc),1/(...

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  3. If a1,a2,a3,...,aaare in A.P then show that 1/(a1a2)+1/(a2a3)+1/(a3a4)...

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  4. If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show...

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  5. Solve :barz=iz^2(z being a complex number)

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  6. if alpha,beta,gamma are in A>P show that cot=(sinalpha-singamma)/(cosg...

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  7. Prove that (1)/(2sin10^(@))-2sin70^(@)=1.

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  8. Prove that 0le3costheta+4sintheta+5le10

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  9. Show that 4(cos^3 10^@+sin^3 20^@)=3(cos10^@+sin20^@)

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  10. If the equation x^2-cx+d=0and x^2-ax+b=0 have a common root,and the ro...

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  11. If alphaand betaare roots of the equation qx^2+px+p=0,show that sqrt(a...

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  12. If z1 and z2 be two complex numbers show that Re(barz1z2)=1/2(z1barz2+...

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  13. Find the sum up to n terms :1+2/3+3/3^2+4/3^3+...

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  14. If x^(1/a)=y^(1/b)=z^(1/c)where a,b,c are in A.P,,than show that x,y,z...

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  15. If (acosthetasecphi-x)/(asin(theta+phi))=(y-bsinthetasecphi)/(bcos(th...

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  16. IF A+B+C=pi,then prove that tan (A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2...

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  17. Prove that secx=2/(sqrt(2+sqrt(2+sqrt(2+2cos8x)))

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  18. Prove that tan20^@+4sin20^@=sqrt3

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  19. A(1,2)and B(5,-2)are two points. P is a point moving in such a way tha...

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  20. A variable straight line passes through the point of intersection of t...

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