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S=sum(i=1)^nsum(j=1)^isum(k=1)^j1...

`S=sum_(i=1)^nsum_(j=1)^isum_(k=1)^j1`

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`sum_(i=1)^(n)sum_(j=1)^(i)sum_(k=1)^(j)1=sum_(i=1)^(n)(i(i+1))/(2)`
`=(1)/(2)[sum_(i=1)^(n)i^(2)+sum_(i=1)^(i)i]=(1)/(2)[sumn^(2)+sumn]`
`=(1)/(2)[(n(n+1)(2n+1))/(6)+(n(n+1))/(2)]`
`=(n(n+1))/(12)[2n+1+3]=(n(n+1)(n+2))/(6)`
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ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. S=sum(i=1)^nsum(j=1)^isum(k=1)^j1

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  2. Let a,b,c be in A.P. and |a|lt1,|b|lt1|c|lt1.ifx=1+a+a^(2)+ . . . ."to...

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  3. Evluate int (tan^(-1)x)/(1+x^2) dx

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  4. If a1, a2, a3, be terms of an A.P. and (a1+a2+.....+ap)/(a1+a2+.....+...

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  5. If a1, a2, a3,.....an are in H.P. and a1 a2+a2 a3+a3 a4+.......a(n-1...

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  6. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

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  7. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  8. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

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  9. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

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  10. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  11. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

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  12. In a G.P of positive terms if any term is equal to the sum of the next...

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  13. Suppose four distinct positive numbers a(1),a(2),a(3),a(4) are in G.P....

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  14. The first two terms of a geometric progression add up to 12. The sum o...

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  15. If the sum of first n terms of an A.P. is cn^(2) then the sum of squar...

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  16. The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is

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  17. Let Sk,k=1, 2, …. 100 denote the sum of the infinite geometric series ...

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  18. Let a1, a2, a3, ,a(11) be real numbers satisfying a1=15 , 27-2a2>0 an...

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  19. Check 2,4,6,8,10 are in A.P or not

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  20. The minimum value of the sum of real numbers a^-5, a^-4, 3a^-3, 1,a^8 ...

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  21. A man saves ₹ 200 in each of the first three months of his servies.In ...

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