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Find the sum of the series 1*n+2*(n-1)+3...

Find the sum of the series `1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n*1` also, find the coefficient of `x^(n-1)` in th cxpansion of `(1+2x+3x^(2)+"...."nx^(n-1))^(2)`.

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JBD PUBLICATION-SEQUENCES AND SERIES-EXAMPLE
  1. The sum of three numbers which are consecutive terms of an A.P. is 21....

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  2. If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c...

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

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  4. The sum of an inifinite G.P. is 8. If the second term is 2, then find ...

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  5. Find the sum to n terms of the series 3 xx 8 + 6 xx 11 + 9 xx 14 + …

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  6. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n...

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  7. The difference between any two consecutive interior angles of a polygo...

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  8. A manufacturer reckons that the value of a machine, which costs him Rs...

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  9. If A.M and G.M of two positive numbers are 13 and 12 respectively. Fin...

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  10. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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  11. The ratio of the sums of m and n terms of an A.P. is m^2: n^2. Show th...

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  12. If a^(2),b^(2),c^(2) are in A.P. Prove that (a)/(b+c),(b)/(c+a),(c)/(a...

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  13. If S(1),S(2),S(3)be respectively the sum of n, 2n and 3n terms of a GP...

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  14. Let S be the sum, P the product and R the sum of reciprocals of n term...

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  15. Let S be the sum, P the product and R the sum of reciprocals of n term...

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

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

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  18. The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from t...

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  19. If a,b,c are in G.P. and x,y are the arithmetic means of a,b and b,c r...

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  20. Find the sum of first n terms of the series. 3+7 + 13 + 21 + 31 + ……...

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