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"Evaluate "Sigma(k=1)^(11) (2+3^(k))...

`"Evaluate "Sigma_(k=1)^(11) (2+3^(k))`

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The correct Answer is:
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`overset(11)underset(k=1)Sigma(2+3^(k))`
`=(2+3)+(2+3^(2))+(2+3^(3))+...+(2+3^(11))`
`=2xx11+(3+3^(2)+3^(3)+...+3^(11))`
`=22+(3(3^(11)-1))/(3-1)=22+265719=265741.`
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NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Exercise 9.3
  1. Find the sum to indicated number of terms in each of the geometric pro...

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  2. Find the sum to indicated number of terms in each of the geometric pro...

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  3. "Evaluate "Sigma(k=1)^(11) (2+3^(k))

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  4. The sum of first three terms of a G.P. is (39)/(10) and their product ...

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  5. How many terms of G.P. 3,3^(2),3^(3),…… are needed to give the sum 120...

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  6. The sum of first three terms of a G.P is 16 and the sum of the next th...

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  7. Given a G.P with a=729 and 7th term 64,determine S(7).

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  8. Find a G.P. for which sum of the first two terms is -4 and the fifth ...

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  9. If the 4th, 10th and 16 th terms of a G.P. are x, y and z, respectivel...

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  10. Find the sum to n terms of the sequence 8,88,888,8888,……

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  11. Find the sum of the product of the corresponding terms of the sequence...

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  12. Show that the products of the corresponding terms of the sequence a,...

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  13. Find four numbers forming a geometric progression in which the third t...

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  14. If the pth, qth and rth terms of a G.P. are a,b and c, respectively. ...

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  15. If the first and the nth term of a G.P. are a and b, respectively, and...

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

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  17. If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b...

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  18. Insert two number between 3 and 81 so that the resulting sequence i...

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  19. Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n)may be the geo...

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  20. The sum of two numbers is 6 times their geometric means, show that nu...

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