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Find the nth terms and the sum to n term...

Find the nth terms and the sum to n term of the series :
`1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2))+...`

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The correct Answer is:
`(n (n +1) ^(2) (n +2))/(12)`
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RESONANCE ENGLISH-SEQUENCE & SERIES -EXERCISE -1 PART -I RMO
  1. The sum of three numbers in A.P. is 27, and their product is 504, find...

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  2. Three friends whose ages form a G.P. divide a certain sum of money in ...

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  3. The roots of the equation x ^(5) - 40 x ^(4) + ax ^(3) + bx ^(2) + cx ...

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  4. Let T(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (l...

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  5. If a, b, c are in A.P. and if (b-c)x^(2)++(c-a)x+a-b=0and2(c+a)x^(2)+(...

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  6. Along a road lies an odd number of stones placed at intervals of 10 m....

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  7. a,b,c are positive real numbers forming a. G.P. If ax ^(2) + 2 bx + c=...

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  8. Determine all pairs (a,b) of real numbers such that 10, a,b,ab are in ...

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  9. 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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  10. If n is any positive integer, then find the number whose square is und...

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  11. Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(1.4.6)...

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

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  13. Find the nth terms and the sum to n term of the series : 1^(2)+(1^(2...

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  14. Let a (j) = (7)/(4) ((2)/(3)) ^( j -1), j in N. lf b (j) = a (j) ^(2...

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  15. The sequence 9, 18, 27, 36, 45, 54,….. consists of successive mutiple ...

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  16. As show in the figure , the five circles are tangent to one another co...

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  17. The arithmaeic mean of the nine numbers in the given set {9,99,999,….....

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  18. Let a sequence whose n^(th) term is {a(n)} be defined as a(1) = 1/2 ...

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  19. If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2...

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  20. Let K is a positive Integer such that 36 +K , 300 + K , 596 + K are th...

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