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Find the sum in the nth group of sequenc...

Find the sum in the nth group of sequence,
(I `1,(2,3),(4,5,6,7),(8,9,………15),………………..`
(ii) `(1),(2,3,4),(5,6,7,8,9),…………..`

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(i) `2^(n-2)(2n^(n)+2^(n-1) -1)`,
(ii) `(n-1)^3 +n^3`.
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MOTION-SEQUENCE & SERIES -Exercise -3 Subjective /JEE Advanced
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  2. If the pth, qth, rth terms of a G. P. be a, b, c respectively, prove t...

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  3. Find the sum in the nth group of sequence, (I 1,(2,3),(4,5,6,7),(8,9...

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  4. Circles are inscribed in the acute angle alpha so that every neighbour...

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  5. If the first 3 consecutive terms of a geometrical progression are the ...

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  6. The sum of three numbers which are consecutive terms of an A.P. is 21....

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  7. The sum of infinite number of terms of a G.P. is 4 and the sum of thei...

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  8. Sum of the following series (i) 1+(2)/(2)+(3)/(2^2)+(4)/(2^3)+……..to...

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  9. The sum of first ten terms of an A.P. is 155 and the sum of first two ...

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  10. In a set of four number, the first three are in GP & the last three ar...

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  11. Find the 4^(th) term of an H.P., whose 7^(th) term is 1/20 and 13^(th)...

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  12. Find the sum of the n terms of the series whose nth term is (i) n(n+...

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  13. Find the sum of the series (5)/(13)+(55)/(13)^2+(555)/(13)^2+(5555)/((...

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  14. If the expression exp {1+|cosx|+cos^(3)x|+cos^(4)x+ . . . . oo)log(e...

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  15. The sum of the infinite series , 1^2- 2^2 / 5+ 3^2 / 5^2 - 4^2 / 5^3 +...

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  16. Find the sum of the n terms of the sequence 1/(1+1^2+1^4)+2/(1+2^2+2^...

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  17. Find the sum of the first n terms ofthe sequence : 1+2(1+1/n)+3(1+1/n)...

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  18. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

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  19. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

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  20. If a1,a,a3...an are in A.P then prove that a1^2-a2^2+a3^2-a4^2+....a(2...

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