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Find the sum of the series: (1xx2xx...

Find the sum of the series:
`(1xx2xx4)+(2xx3xx7)+(3xx4xx10)+... "to n terms" `

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Verified by Experts

The correct Answer is:
`(n(n+1)(3n^(2)+19n+14))/(12)`
`T_(n) = ("nth term of "1,2,3, ...)xx("nth term of "2,3,4,...)xx("nth term of "4,7,10,...)`
`=n(n+1)xx[4+(n-1)xx3]=n(n+1)(3n+1)=(3n^(3)+4n^(2)+n).`
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RS AGGARWAL-SOME SPECIAL SERIES-EXERCISE 13A
  1. Find the sum of n terms of the series whose nth term is: n^3-3^n

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  2. Find the sum of the series: (2^(2)+4^(2)+6^(2)+8^(2)+ ..."to n te...

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  3. Find the sum of the following series to n term: 2^3+4^3+6^3+8^3+

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  4. Find the sum to n terms of the series :5^2+6^2+7^2+dotdotdot+20^2

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  5. Find the sum to n terms of the series 1xx2+2xx3+ 3xx4+ 4xx5+......

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  6. Find the sum to n terms of the series :3xx8+6xx11+9xx14+dotdotdot

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  7. Find the sum of the series: 1xx2^(2)+2xx3^(2)+3xx4^(2)+... "to n ...

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  8. Find the sum of the series: 1xx2^(2)+3xx3^(2)+5xx4^(2)+... "to n ...

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  9. Find the sum of the following series to n term: 3xx1^2+5xx2^2+7xx3^2+

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  10. Find the sum to n terms of the series :1xx2xx3 + 2xx3xx4 + 3xx4xx5 + d...

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  11. Find the sum of the series: (1xx2xx4)+(2xx3xx7)+(3xx4xx10)+... "t...

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  12. Find the sum to n terms of the series :1/(1xx2)+1/(2xx3)+1/(3xx4)+dotd...

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  13. Find the sum of the series: (1)/((1xx3))+(1)/((3xx5))+(1)/((5xx7)...

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  14. Sum the following series to n terms: 1/(1. 6)+1/(6. 11)+1/(11. 16)+1/(...

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  15. Find the sum of the series (1^3)/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3+...

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  16. Find the sum to n terms of the series 3+15+35+63+

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  17. Find the sum to n terms of the series: 1+5+12+22+35+

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  18. Find the sum of the following series to n terms 5+7+13+31+85+

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  19. If Sk=(1+2+3+...k)/k then find the value of S1^2+S2^2+....Sn^2

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  20. let S(n) denote the sum of the cubes of the first n natureal number...

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