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If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) wher...

If `(1+3+5++p)+(1+3+5++q)=(1+3+5++r)` where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of `p+q+r(w h e r ep >6)` is `12` b. `21` c. `45` d. `54`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
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  2. Let Tr a n dSr be the rth term and sum up to rth term of a series, res...

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  3. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

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  4. If a x^3+b x^2+c x+d is divisible by a x^2+c ,t h e na ,b ,c ,d are in...

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  5. If the lines 3x + by + 5 = 0 and ax – 5y + 7 = 0 are perpendicular to ...

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  6. In a geometric series, the first term is a and common ratio is rdot If...

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  7. If x ,y ,a n dz are distinct prime numbers, then (a).x , y , a n dz ma...

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  8. If x ,y , and z are in G.P. and x+3,y+3, and z+3 are in H.P., then a.y...

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  9. If A.M., G.M., and H.M. of the first and last terms of the series of 1...

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  10. The sum 1+3+7+15+31+...to100 terms is a. 2^(100)-102 b. 2^(99)-101 c...

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  11. The sum of first 15 terms of an A.P. is 750 and its first term is 15. ...

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  12. The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^...

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  13. Let S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo . Then s is equal to a....

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  14. If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...

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  15. If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then val...

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  16. The sum o f series 1+4/5+7/(5^2)+(10)/(5^3)+oo is a. 7//16 b. 5//16 ...

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  17. The sum 20 terms of a series whose rth term is given by Tr=(-1)^r((r^2...

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  18. Consider the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th te...

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  19. If the first term of an A.P. is – 18 and its 10th term is zero, then f...

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  20. Suppose that F(n + 1) =(2F(n) + 1)/2 for n = 1,2,3,,,, and F(1) = 2. T...

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