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If a1,a2,a3, ,an are an A.P. of non-ze...

If `a_1,a_2,a_3, ,a_n` are an A.P. of non-zero terms, prove that `1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)=`

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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)) .

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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))

Let r be the common ratio of the GP a_1,a_2,a_3,....,a_n . Show that 1/(a_1^m+a_2^m)+1/(a_2^m+a_3^m)+....+1/(a_(n-1)^m+a_n^m)=(1-r^((1-n)m))/(a_1^m(r^m-r^-m)) .

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If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : 1+a_1+a_2+…+a_(n-1) =0.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE 9 (a) LATQ
  1. Find the terms indicated in each case: (i) a(n)=4n-3,a(17),a(24) ...

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  2. Find the terms (s) indicated in each case: (i) t(n)=t(n-1)+3(ngt1),t...

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  3. Write the first five terms of the sequence and obtain the correspondi...

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  4. Write the first six terms of each of following sequences, (i) a(1)=-...

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  5. The sequence a(n)is defined by: a(n)=(n-1)(n-2)(n-3). Show that th...

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  6. a. Find the 21 st and 42 nd terms of the sequence defined by: t(n)=...

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  7. If a0=1,a1=3 and an^2 -a(n-1)*a(n+1)=(-1)^n. Find a3.

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  8. Consider the sequence defined by t(n)=an^(2)+bn+c If t(2)=3,t(4)=13 an...

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  9. The third term of an A.P. is 25 and the tenth term is -3. find the fir...

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  10. (i) The 3rd term of an A.P. is 1 and 6 th term is -11. Determine its ...

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  11. The mth term of an A.P. is (1)/(n) and nth term is (1)/(m). Its (mn)th...

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  12. The fourth term of an A.P. is equal to 3 times the first term and seve...

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  13. The 2 nd,31st and last terms of an A.P.are 7 3/4, 1/2 and -6 1/2 respe...

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  14. (i) The pth term of an A.P. is q the 1th term is p, show that rth ter...

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  15. If pth term of an A.P. is c and the qth term is d, what is the rth ter...

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  16. For the A.P., a(1),a(2),a(3),…………… if (a(4))/(a(7))=2/3, find (a(6))/(...

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  17. If a1,a2,a3, ,an are an A.P. of non-zero terms, prove that 1/(a1a2)+...

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  18. If a(1),a-(2),a(3),………….a(n) are in A.P. with common differecne d, pro...

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  19. A man serves Rs. 320 in the month of January Rs. 360 in the month of F...

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  20. If m times the m^(t h) term of an A.P. is equal to n times its n^(t h)...

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