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Find the sum of the following series who...

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

Text Solution

Verified by Experts

Given that `T_n=(2n-1)^2`
`T_n=4n^2+1-4n`
`S_1= sum T_N= sum (4n^2+1-4n)`
`4((n(n+1)(2n+1))/6)+n-(4n(n+1))/2`
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RD SHARMA-SOME SPECIAL SERIES-Solved Examples And Exercises
  1. Find the sum of the following series whose n t h term is: n^3-3^ndot

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

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

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

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

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

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

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

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  9. Sum of the following series to n term: 1+3+7+13+21+ ............

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  10. Sum of the following series to n term: \ 1+3+6+10+15+.............

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  11. Sum of the following series to n term: 1/(1* 4)+1/(4* 7)+1/(7*10)+ ......

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  12. Find the sum 2+5+10+17+26+. . . .

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  13. Find the sum of the series 3+7+14+24+37..

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  14. Sum of the following series to n term: 2+4+7+11+16+.......

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  15. Write the sum of the series 2+4+6+8+...........+2n

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  16. Write the sum of the series 1^2-2^2+3^2-4^2+5^2-6^2...........+(2n-1)^...

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  17. Write the sum of n term for a series whose r^(t h) term is: r+2^r.

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  18. If sum(r=1)^n r=55 ,find sum(r=1)^n r^3.

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  19. If the sum of first n even natural numbers is equal to k times the sum...

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  20. Write the sum of 20 terms of the series: 1+1/2(1+2)+1/3(1+2+3)+

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