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The sum of the first n terms of the seri...

The sum of the first n terms of the series `(1)/(2)+(3)/(4)+(7)/(8)+(15)/(16)+....` is equal to

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The correct Answer is:
`n + 2^(–n) – 1`
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CBSE COMPLEMENTARY MATERIAL-SEQUENCES AND SERIES -SECTION-D (LONG ANSWER TYPE QUESTIONS )
  1. Prove that the sum of n numbers between a and b such that then(a + b)r...

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  2. A square is drawn by joining the mid points of the sides of a square. ...

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  3. If a, b, c are in G.P., then prove that (1)/(a^(2)-b^(2))-(1)/(b^(2)-c...

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  4. Find two positive numbers whose difference is 12 an whose A.M. exce...

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  5. If a is A.M. of b and c and c,G(1),G(2),b are in G.P., then find the v...

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  6. Find the sum of the series,1.3.4 + 5.7.8 + 9.11.12 +.............. upt...

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  7. Evaluatesum1^10(2r-1)^2

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  8. The sum of an infinite GP is 57 and the sum of their cubes is 9747. Fi...

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  9. If (10)^9 + 2(11)^1 (10)^8 + 3(11)^2 (10)^7+...........+10 (11)^9= k ...

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  10. The sum of the first n terms of the series (1)/(2)+(3)/(4)+(7)/(8)+(15...

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  11. Three positive numbers form an increasing GP. If the middle term in th...

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  12. If a,b,c are in AP, show that 1/((sqrtb+sqrtc)),1/((sqrtc+sqrta)),1/...

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  13. Find the sum of the series 1-3/2+5/4-7/8+9/16..........oo

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  14. In the sum of first n terms of an A.P. is cn^2, then the sum of square...

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  15. Let pa n dq be the roots of the equation x^2-2x+A=0 and let ra n ds be...

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  16. If S(1), S(2), S(3),...,S(n) are the sums of infinite geometric series...

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  17. If the m th, n th and p th terms of an AP and GP are equal and are x ,...

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  18. The sum of an infinite GP is 57 and the sum of their cubes is 9747. Fi...

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  19. Find three numbers in G.P. whose sum is 13 and the sum of whose square...

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