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If S1, S2, S3 are the sums of first n na...

If `S_1, S_2, S_3` are the sums of first `n` natural numbers, their squares and cubes respectively, show that `9S_2^ 2=S_3(1+8S_1)dot`

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`S_1=((n(n+1))/2`
`1+8S_1=4n(n+1)+1=(2n+1)^2`
`S_2=(n(n+1)(2n+1))/6`
`S_3=((n(n+1))/2)^2`
...
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RD SHARMA-SOME SPECIAL SERIES-Solved Examples And Exercises
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  2. Show that (1xx2^2+2xx3^2+. . . +nxx(n+1)^2)/(1^2xx2+2^2xx3+. . . +n^2x...

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

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

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

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

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

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

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  10. Find the sum to 10 terms of the series 1xx2+2xx3+ 3xx4+ 4xx5+......

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

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

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

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  14. Find the sum of the following series whose n th term is: n(n+1)(n+4)

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  15. Find the sum of the following series whose n th term is: (2n-1)^2

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

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

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

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

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  20. Sum of the following series to n term: 3+5+9+15\ +23+........

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