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If S(1),S(2),S(3),"....",S(p) are the su...

If `S_(1),S_(2),S_(3),"....",S_(p)` are the sums of n terms of p AP's whose first terms are `1,2,3,"…",p` and common differences are `1,2,3,"…",(2p-1)` respectively, show that `S_(1)+S_(2)+S_(3)+"...."+S_(p)=(1)/(2)np(np+1).`

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

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  2. If Sn denotes the sum of n terms of an A.P. whose first term is a, and...

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  3. If S(1),S(2),S(3),"....",S(p) are the sums of n terms of p AP's whose ...

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  4. If the sum of m terms of an AP is equal to the sum of either the next ...

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  5. If the sum of first p terms of an A.P. is equal to the sum of the firs...

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  6. The first term of an A.P. is a, the second term is b and last term is ...

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  7. Find the sum of all numbers in the first 1000 integers, which are neit...

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  8. A man gets an appointment with two options Either he can accept ₹ 45 p...

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  9. A farmer, 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 22000 He pays Rs. 4000 cash And ag...

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

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

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

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  15. If a(1)=1, a(2)=5 find the common difference and 5th term of A.P

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  16. If the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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

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  19. If the mth, nth and pth terms of a G.P. form three consecutive terms o...

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  20. If x,y,z are in G.P. and a^x= b^y=c^z, prove that logb a. logb c=1.

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