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Find the sum: sum(n=1)^(10){(1/2)^(n-1)+...

Find the sum: `sum_(n=1)^(10){(1/2)^(n-1)+(1/5)^(n+1)}dot`

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. Let an be the nth term of a G.P. of positive numbers. Let sum(n=1)^(10...

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  2. The fifth term of a G.P. is 81 whereas its second term is 24. Find the...

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  3. Find the sum: sum(n=1)^(10){(1/2)^(n-1)+(1/5)^(n+1)}dot

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  4. If S1, S2, ,Sn are the sum of n term of n G.P., whose first term is 1...

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  5. If S1, S2, S3 be respectively the sums of n ,2n ,3n terms of a G.P., t...

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  6. Find the least value of n for which the sum 1+3+3^2+ ton terms is gr...

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  7. Prove that the sum of n terms of the series: 11+103+1005+ i s(10)/9(10...

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  8. How many terms of the sequence sqrt(3),3,3sqrt(3) must be taken to mak...

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  9. How many terms of the G.P. 3,3//2,3//4, be taken together to make (30...

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  10. If a ,b ,c ,d are in A.P. and x , y , z are in G.P., then show that x^...

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  11. If a ,b ,c ,d are in G.P., prove that a+b,b+c ,c+d are also in G.P.

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  12. If a ,b ,c are in G.P., then prove that loga^n ,logb^n ,logc^n are in ...

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  13. If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G....

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  14. If S denotes the sum of an infinite G.P. adn S1 denotes the sum of the...

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  15. The sum of first two terms of an infinite G.P. is 5 and each term is ...

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  16. One side of an equilateral triangle is 18 cm. The mid-point of its ...

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  17. If Sp denotes the sum of the series 1+r^p+r^(2p)+... tooo and S(p') t...

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  18. If each term of an infinite G.P. is twice the sum of the terms foll...

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  19. If |x|<1a n d|y|<1, find the sum of infinity of the following series:...

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  20. Find the sum of n terms of the sequence (x+1/x)^2,(x^2+1/(x^2))^2,(x^3...

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