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Show that the sum of the cubes of any nu...

Show that the sum of the cubes of any number of consecutive integers is divisible by sum of those integers.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Find the sum of n terms of the series whose nth term is given by n^2+2...

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  2. Find the sum Sn of the cubes of the first n terms of an A.P. and show ...

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  3. Show that the sum of the cubes of any number of consecutive integers i...

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  4. An odd of stones lie along a straight path, the distance between any t...

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  5. Find the sum of n terms of the following series : 1+3+6+10 +...........

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  6. Find the sum of n terms of the following series : 2+5+10+ 17+ .........

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  7. Find the sum of n terms of the following series : 1+3+7+13 +......

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  8. Find the sum of n terms of the following series : 1+5+13+29+61+ .......

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  9. Find the sum of n terms of the following series : 1+3+7+15+31 +........

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  10. Find the sum of n terms of the following series : 7+77+777 +......

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  11. Find the sum of n terms of the following series : 5+11+19+29+41+ ......

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  12. Find the sum of first n terms of the series. 3+7 + 13 + 21 + 31 + ……...

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  13. Find the sum of n terms of the series whose nth term is : 2^(n-1)-1.

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  14. Find the sum of n terms of the series whose nth term is : 2^(n+1)+4(...

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  15. Write the first six terms of the following sequence : a(1)=a(2)=1, a(n...

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  16. Which term of the progression 19 , 18 1/5, 17 2/5, ......... is the fi...

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  17. Each term of an A.P. is doubled. Is the resulting sequence also an A.P...

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  18. In an A.P., the mth term is 1/n and the nth term is 1/m, find the (mn)...

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  19. If a, b, c are in A.P., then prove that : (a-c)^2 =4(b^2 -ac).

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  20. Show that the sequence : log a, log (ab), log (ab^2), log (ab^3),........

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