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Natural numbers are written as 1, (2,3),...

Natural numbers are written as 1, (2,3), (4,5,6)..
Show that the sum of number in the nth group is `(n)/(2) (n +1)` .

A

62525

B

65255

C

56255

D

55625

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A
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. Two sequences lta(n)gtandltb(n)gt are defined by a(n)=log((5^(n+1))/...

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  2. The sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1...

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  3. Natural numbers are written as 1, (2,3), (4,5,6).. Show that the sum...

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  4. If the first term of an A.P. is 2 and common difference is 4, then ...

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  5. If 1+(1+2)/2+(1+2+3)/3+ddotto\ n terms is Sdot Then, S is equal to (n(...

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  6. The sum of 10 terms of the series sqrt(2)+sqrt(6)+sqrt(18)+ddoti s\ ...

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  7. The (m+n)th and (m-n)th terms of a GP are p and q, respectively. Then,...

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  8. The fourth, seventh and tenth terms of a G.P. are p,q,r respectively, ...

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  9. The sum of the integers from 1 to 100 which are not divisible by 3 or ...

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  10. Let the harmonic mean and geometric mean of two positive numbers be in...

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  11. The sum of the series 1 + 2.2+ 3.2^(2) + 4.2^(3) + 5.2^(4) + ….. +...

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  12. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

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  13. If the m^(th),n^(th)andp^(th) terms of an A.P. and G.P. be equal and b...

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  14. The 7th term of a H.P. is (1)/(10) and 12 th term is (1)/(25), find th...

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  15. The length of side of a square is 'a' metre. A second square is formed...

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  16. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

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  17. If three positive real numbers a,b,c, (cgta) are in H.P., then log(a+c...

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  18. In an A.P., the p^(th) term is 1/q and the q^(th) term is 1/p. fin...

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  19. The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n...

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  20. If a,b,c are in H.P. , then

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