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Show that (1xx2^2+2xx3^2+dotdotdot+nxx(n...

Show that `(1xx2^2+2xx3^2+dotdotdot+nxx(n+1)^2)/(1^2xx2+2^2xx3+dotdotdot+n^2xx(n+1))=(3n+5)/(3n+1)dot`

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RD SHARMA ENGLISH-SOME SPECIAL SERIES-All Questions
  1. Find the sum to n terms of the series whose nth term is n^2+2^n.

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  2. 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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  3. Show that (1xx2^2+2xx3^2+dotdotdot+nxx(n+1)^2)/(1^2xx2+2^2xx3+dotdotdo...

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  4. If S1, S2, S3 are the sums of first n natural numbers, their squares a...

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  5. Find the sum to n terms of the series :1^2+(1^2+2^2)+(1^2+2^2+3^2)+......

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  6. The sequence N of natural numbers is divided into classes as follows. ...

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  7. Find the sum of the following series to n term: 1^3+3^3+5^3+7^3+.........

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

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  9. Find the sum of the following series to n term: 1. 2. 5+2. 3. 6+3. 4. ...

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  10. Find the sum of the following series to n term: 1. 2. 4+2. 3. 7+3. 4. ...

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

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

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  13. Find the sum of the following series whose n t h term is: 2n^3+3n^2-1.

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  14. Find the sum of the following series whose n t h term is: n^3-3^ndot

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  15. Find the sum of the following series whose n t h term is: n(n+1)(n+4)d...

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  16. Find the sum of the following series whose n t h term is: (2n-1)^2dot

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  17. Find the 20th term and the sum of 20 terms of the series: 2xx4+4xx6+6x...

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  18. Find the sum of the first n terms of the series : 3 + 7 + 13 +21 + 31...

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  19. Find the sum of first n terms of the following series:5+11+19+29+41+.....

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  20. Find the sum of n terms\ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+.....

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