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Sum to n terms: 0.5+0.55 + 0.555 +......

Sum to n terms:
0.5+0.55 + 0.555 +...

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Statement -1 For all natural numbers n , 0.5+0.55+0.555+...... upto n terms =(5)/(9){n-(1)/(9)(1-(1)/(10^n))} , Statement-2 a+ar+ar^2+....+ar^(n-1)=(a(1-r^n))/((1-r)) , for 0lt r lt 1 .

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Use geometric series to express 0.555 = 0.5 as a rational number .

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Find the sum to n terms 0.6 + 0.66 + 0.666 + ………..

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  2. Sum to n terms: 0.3+ 0.33 +0.333 +.......

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  3. Sum to n terms: 0.5+0.55 + 0.555 +...

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  4. Find the sum to n terms 0.6 + 0.66 + 0.666 + ………..

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  5. If 1/(1+l)=v, prove that : v+v^(2)+v^(3)+………+v^(n)=(1-v^(n))/l.

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  6. Find the sum to n terms of the sequence : 1,-1,1,-1,........ ,(-1)^(n+...

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  7. If the sum of first 10 terms is 33 times the sum of first 5 terms of G...

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  8. Show that the ratio of the sum of first n terms of a G.P. to the sum o...

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  9. Find the sum of the products of the corresponding terms of the sequenc...

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  10. If S1,S2,S3 be the sum of n, 2n, 3n terms of a G.P., show that : S1(S3...

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  11. An inventor of the chess board suggested a reward of one grain of whea...

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  12. Dipesh writes letters to four of his friends. He asks each of them to ...

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  13. A machine is depreciated at the rate of 10 % yearly and the ultimate s...

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  14. Insert two numbers between 3 and 81 so that the resulting sequence is ...

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  15. Insert 4 geometric means between 6 and 192.

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  16. The A.M. between two numbers is 20 and their G.M. is 16. Find the numb...

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  17. a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c r...

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  18. a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c r...

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  19. The sum of two numbers is 6 times their geometric mean, show that numb...

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  20. The ratio of the.A.M. and G.M. of two positive numbers a and b is m : ...

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