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Sum the following series to n terms: 5+7...

Sum the following series to `n` terms: `5+7+13+31+85+`

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To find the sum of the series \( S_n = 5 + 7 + 13 + 31 + 85 + \ldots \) up to \( n \) terms, we will follow these steps: ### Step 1: Identify the pattern in the series The given series is: - \( t_1 = 5 \) - \( t_2 = 7 \) - \( t_3 = 13 \) - \( t_4 = 31 \) ...
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RD SHARMA ENGLISH-SOME SPECIAL SERIES-All Questions
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  2. Find the sum to n terms of the series: 3/(1^2 .2^2)+5/(2^2 .3^2)+7/(3^...

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  3. Sum the following series to n terms: 5+7+13+31+85+

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  4. Find the sum to n terms of the series: 1/(1. 3)+1/(3. 5)+1/(5. 7)+

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

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

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  7. Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

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  8. Find the sum of series (3^3-2^3)+(5^3-4^3)+(7^3-6^3)+... n terms.

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  9. If Sn=sum(r=1)^n(1+2+2^2+ .......+2^r)/(2^r), then Sn is equal to (a)2...

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  10. The value of sum(r=1)^n{(2r-1)a+1/(b^r)} is equal to (a)a n^2+(b^(n-...

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  11. The sum of the series: 1/((log)2 4)+1/((log)4 4)+1/((log)8 4)++1/((log...

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  12. The sum n terms of the series 1/(sqrt(1)+sqrt(3))+1/(sqrt(3)+sqrt(5))+...

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  13. Find the sum of n terms of the series 1*2*3+2*3*4+3*4*5...........

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  14. Sum the series 3. 8+6. 11+9. 14+............... to n terms.

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  15. Find the sum of n terms of the series whose n t h term is: 2n^2-3n+5

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  16. Find the sum to n terms of the series whose nth term is n^2+2^n.

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

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

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  20. 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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