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If a1,a2,a3, ,an are in A.P., where ai >...

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)) .

NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Exercise 9B
  1. (a) The nth term of a progression is (3n + 5). Prove that this progres...

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  2. (a) Find the 10th term of the progression 1 + 3 + 5 +7+ ... (b) Find...

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  3. (a) Which term of the progression 4 + 8 + 12 + ... is 76 ? (b) Which...

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  4. (a) Find the 16th term from the end of the progression 3 + 6 + 9 + ......

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  5. (a) How many numbers of two digits are divisible by 3 ? (b) How man...

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  6. (a) Find the value of 'x if x + 1, 2x + 1 and x + 1 are in A.P. Also f...

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  7. (a) The 3rd and 19th terms of an A.P. are 13 and 77 respectively. Find...

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  8. If (p + 1)th term of an A.P. is twice the (q + 1)th term, then prove t...

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  9. The 12th term of an A.P. is 14 more than the 5th term. The sum of thes...

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  10. (a) Is 303, a term of the progression 5, 10, 15, ... ? (b) Is 38, a...

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  11. In an A.P., prove that : T(m+n) + T(m-n) = 2*T(m)

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  12. (i) 10 times the 10th term and 15 times the 15th term of an A.P. are e...

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  13. Which term of the A.P. (16-6i,)(15-4i), (14-2 i), ... is a : (a) pur...

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  14. (a) Which term of the progression 10,9(1)/(3),8 (2)/(3),...is the firs...

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  15. Each of two arithmetic progressions 2, 4, 6, ... and 3, 6, 9, ... are ...

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

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  17. If the numbers a, b, c, d, e are in arithmetic progression then find t...

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