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If S1,S2, S3, Sm are the sums of n terms...

If `S_1,S_2, S_3, S_m` are the sums of `n` terms of `m` A.P. `' s` whose first terms are `1,2,3, ,m` and common differences are `1,3,5, ,(2m-1)` respectively. Show that `S_1+S_2,+S_m=(m n)/2(m n+1)`

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MODERN PUBLICATION-SEQUENCES AND SERIES-REVESION EXERCISE
  1. How many numbers of two digits are divisible by 7?

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  2. Let S(n) denotes the sum to terms of an A.P. whose first term is a . I...

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  3. If S1,S2, S3, Sm are the sums of n terms of m A.P. ' s whose first ter...

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  4. If the sum of m terms of an A.P. is equal to the sum of either the nex...

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  5. IF the sum of p terms of an AP is q and the sum of q terms is ...

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  6. In a G.P. the first term is a, second term is b and the last term is ...

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  7. Find the sum of all natural numbers between 1 and 100, which are divis...

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  8. A man gets an appointment with two options. Either he can accept Rs. 4...

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  9. A fanner buys a used tractor for Rs 12000. He pays Rs 6000 cash and...

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  10. Shamshad Ali buys a scooter for Rs. 2200. He pays Rs. 4000 cash and ...

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  11. Two cars start together in the same direction from the same place. The...

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  12. The ages of the students of a class form an A.P. whose common differen...

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  13. "If " a^(2), b^(2), c^(2)" are in A.P., prove that "(1)/(b+c),(1)/(c+a...

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  14. If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P. then show that b=(2ac)/(a+c...

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  15. if the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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  16. If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

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  17. If a^2(b+c),b^2(c+a),c^2(a+b), are in A.P. show that either a ,b ,c ar...

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  18. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

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

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

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