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Find the sum to infinity of this geometr...

Find the sum to infinity of this geometric progression.
`1,1/2,1/2^2,1/2^3,……`

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Find the sum to infinity of this geometric progression. 5,20/7,80/49,……

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If the sum of the first n terms of an Arithmetic progression is S_n=nX+1/2n(n-1)Y where X and Y are constants, find S_1 and S_2 .

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MAXIMUM PUBLICATION-SEQUENCE AND SERIES-EXAMPLE
  1. The third term of a GP is 4. Find the product of the first five terms.

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  2. Insert 4 geometric means between 4 and 972.

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  3. Find the sum to infinity of this geometric progression. 1,1/2,1/2^2,...

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  4. Find the sum to infinity of this geometric progression. 5,20/7,80/49...

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  5. The 10^th term of an AP is 73 and the 20^thterm is 43. Find the 44^th ...

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  6. The 7^th term of an AP is 34 and the 15^thterm is 74. Find the 40^th t...

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  7. Find the sum of 32 terms of an AP whose third term is 1 and the 6^th t...

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  8. Find the sum to n terms of a series is 7n^2-5n. Show that it is an AP ...

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  9. Find three numbers in AP whose sum is -3 and whose product is 8.

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  10. Find the three numbers in AP whose sum is 21 and product is 231.

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  11. Find the sum of all natural numbers between 100 and 1000 which are mul...

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  12. If the AM and GM between two numbers are 34 and 16 respectively. Find ...

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  13. If the p^th,q^th and r^th terms of a GP are a,b,c respectively, show t...

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  14. The sum of the first p,q,r terms of an AP are a,b,c respectively, prov...

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  15. The ratio between the sums to n terms of two AP is 7n+1:4n+27. Find th...

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  16. If the sum of p terms of an AP is the same as the sum of its q terms, ...

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  17. The sum of the first two terms of a GP Is -4 and the fifth term is 4 t...

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  18. The sum of the first two terms of a GP Is -4 and the fifth term is 4 t...

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  19. The sum of three numbers in GP is 38 and their product is 1728. Find t...

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  20. Find the three numbers in GP whose sum is 13 and the sum of whose squa...

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