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Evaluate underset(k=1)overset(11)Sigma (...

Evaluate `underset(k=1)overset(11)Sigma (2 + 3^(k))`

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The correct Answer is:
`22 + (3)/(2) (3^(11)-1)`
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Suppose a_(1), a_(2), a_(3),…., a_(49) are in A.P and underset(k=0)overset(12)Sigma a_(4k+1)= 416 and a_(9) + a_(43)= 66 . If a_(1)^(2) + a_(2)^(2)+ ….+ a_(17)^(2)= 140m then m= ……..

If x= underset(n=0)overset(oo)Sigma cos^(2n) phi, y= underset(n=0)overset(oo)Sigma sin^(2n) phi and z= underset(n=0)overset(oo)Sigma cos^(2n) phi .sin^(2n) phi , where 0 lt phi lt (pi)/(2) then prove that, xy+z= xyz .

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If (a_(1),1,1),(1,a_(2),1) and (1,1,a_(3)) are coplaner (where a_(i)ge1,i=1,2,3) then underset(i=1)overset(3)sum(1)/(1-a_(i)) = …………..

KUMAR 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 underset(k=1)overset(11)Sigma (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 t...

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  7. Given a G.P. with a = 729 and 7^("th") term 64, determine S7 .

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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 16th terms of a G.P. are x, y and z, respectively...

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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 products of the corresponding terms of the sequenc...

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  12. Show that the products of the corresponding terms of the sequences 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 p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and ...

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  15. If the first and the n^("th") term of a G.P. are a and b, respectivel...

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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...

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

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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 ...

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

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