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If `a_1,a_2,a_3, ,a_n` are in A.P., where `a_i >0` for all `i` , show that `1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot`

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If a_1,a_2,a_3,………a_n are in A.P, where a_igt0 for all i 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 a_1,a_2,a_3,.....,a_n are in AP where a_i ne kpi for all i , prove that cosec a_1* cosec a_2+ cosec a_2* cosec a_3+...+ cosec a_(n-1)* cosec a_n=(cota_1-cota_n)/(sin(a_2-a_1)) .

If a_1,a_2,a_3,…………..a_n are in A.P. whose common difference is d, show tht sum_2^ntan^-1 d/(1+a_(n-1)a_n)= tan^-1 ((a_n-a_1)/(1+a_na_n))

If a_1,a_2,a_3,.....,a_n are in AP, prove 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_3,...,a_n are in AP and a_i ne (2k-1)pi/2 for all i , find the sum seca_1*seca_2+seca_2*seca_3+seca_3*seca_4+...+seca_(n-1)*seca_n .

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : (1-a_1)(1-a_2)(1-a_3)...(1-a_(n-1)) =n.

If the nonzero numbers a_1,a_2,a_3,....,a_n are in AP, prove that 1/(a_1a_2a_3)+1/(a_2a_3a_4)+...+1/(a_(n-2)a_(n-1)a_n)=1/(2(a_2-a_1))(1/(a_1a_2)-1/(a_(n-1)a_n)) .

MODERN PUBLICATION-SEQUENCES AND SERIES-REVESION EXERCISE
  1. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

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  2. If x,y,z are in G.P and a^x=b^y=c^z,then

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  3. We are given two G.P's one with the first term a and common ratio r an...

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  4. if sn, denotes the sum of n terms of a GP whose first term and common ...

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  5. If p, q, r are in G.P. and the equations, p x^2+2q x+r=0and dx^2+2e x...

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  6. If S(n) denotes the sum of n terms of a G.P., prove that: (S(10)-S(20)...

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  7. The sum of the first thre consecutive terms of G.P is 13 and the sum o...

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  8. If 1/(a+b)+1/(b+c)=1/b, prove that a,b,c are in G.P.

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  9. 150 workers were engaged to finish a job in a certain number of days. ...

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  10. If |x|<1a n d|y|<1, find the sum of infinity of the following series: ...

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  11. A manufacture reckons that the value of a machine which costs him Rs. ...

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  12. The sum of the series : 1+1/(1+2)+1/(1+2+3)+...... upto 10 terms is :

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  13. Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

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  14. Obtain the sum of the series 1/4+1/16+1/64……………….to oo

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  15. Show that (1xx2^2+2xx3^2+dotdotdot+nxx(n+1)^2)/(1^2xx2+2^2xx3+dotdotdo...

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  16. What will Rs. 500 amounts to in 10 years after its deposit in a bank w...

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  17. A man deposited Rs 10000 in a bank at the rate of 5% simple interes...

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  18. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/(sqr...

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  19. if S is the sum , P the product and R the sum of reciprocals of n term...

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  20. A thief runs with a uniform speed of 100 m/min. After one minute a pol...

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