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If `(1 ^(2) - t _(1)) + (2 ^(2) - t _(2)) + ......+ ( n ^(2) - t _(n)) =(1)/(3) n ( n ^(2) -1 ),` then `t _(n)` is

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RESONANCE ENGLISH-SEQUENCE & SERIES -EXERCISE -1 PART -I RMO
  1. The sum of the series 1.2 + 2.3+ 3.4+…….. up to 20 tems is

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  2. sum (r = 2) ^(oo) (1)/(r ^(2) - 1) is equal to :

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  3. If (1 ^(2) - t (1)) + (2 ^(2) - t (2)) + ......+ ( n ^(2) - t (n)) =(...

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  4. If x gt 0, then the expression (x ^(100))/( 1 + x + x ^(2) +x ^(3) + ....

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  5. Given the sequence a, ab, aab, aabb, aaabb,aaabbb,…. Upto 2004 terms, ...

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  6. The first two terms of a sequence are 0 and 1, The n ^(th) terms T (n)...

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  7. Consider the following sequence :a (1) = a (2) =1, a (i) = 1 + minimum...

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  8. The sum of (1)/( 2sqrt1+1 sqrt2 ) + (1)/( 3 sqrt2 + 2 sqrt3 ) + (1)/(...

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  9. If f (x) + f (1 - x) is equal to 10 for all real numbers x then f ((1)...

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  10. For some natural number 'n', the sum of the first 'n' natural numbers ...

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  11. An arithmetical progression has positive terms. The ratio of the diffe...

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  12. The 12 numbers, a (1), a (2)………, a (12) are in arithmetical progressio...

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  13. Each term of a sequence is the sum of its preceding two terms from the...

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  14. n is a natural number. It is given that (n +20) + (n +21) + ......+ (n...

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  15. In a G.P. of real numbers, the sum of the first two terms is 7. The su...

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  16. In a potato race, a bucket is placed at the starting point, which is 7...

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  17. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

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

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  19. The sum of three numbers in A.P. is 27, and their product is 504, find...

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

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