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The sum of series 1+6+(9(1^(2)+2^(2)+...

The sum of series
`1+6+(9(1^(2)+2^(2)+3^(2)))/(7) + (12(1^(2)+2^(2)+3^(2)+4^(2)))/(9)+(15(1^(2)+2^(2)+...+5^(2)))/(11)+...` up to 15 terms is

A

7520

B

7510

C

7830

D

7820

Text Solution

Verified by Experts

The correct Answer is:
D
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Find sum of first 15 term of series 1+6+(9(1^(2)+2^(2)+3^(2)))/(7)+(12(1^(2)+2^(2)+3^(2)+4^(2)))/(9) (1) 7620 (2) 7280 (3) 7820 (4) 7067

The sum to n terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1^(2)+2^(2)+3^(2))+--

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(1^(2)-2^(2)+3^(2)) + (4^(2)-5^(2)+6^(2))+(7^(2)-8^(2)+9^(2))….30 terms

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Let S_(n) be the sum to n terms of the series (2)/(1 ^(2)) + (5)/(1 ^(2) + 2^(2)) + (7)/(1^(2) + 2^(2) + 3^(2)) + (9)/(1 ^(2) + 2^(2) + 3 ^(2) + 6 ^(2))+ ……. then

(5) / (3 ^ (2) 7 ^ (2)) + (9) / (7 ^ (2) 11 ^ (2)) + (13) / (11 ^ (2) 15 ^ (2)) + .... oo

The sum of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1^(2)+2^(2)+3^(2))+...... upto n terms,is

Sum of n terms the series: 1^(2)-2^(2)+3^(2)-4^(2)+5^(2)-6^(2)+

MCGROW HILL PUBLICATION-PROGRESSIONS-Questions from Previous Years. AIEEE/JEE Main Papers
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  3. The sum of series 1+6+(9(1^(2)+2^(2)+3^(2)))/(7) + (12(1^(2)+2^(2)+...

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  10. The product of three consecutive terms of a G.P. is 512. If 4 is added...

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  12. If 19^(th) term of a non-zero A.P. is zero, then (49^(th) term) : (29^...

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  13. The sum of all natural numbers 'n' such that 100 lt n lt 200 and HCF (...

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  14. The sum underset(k=1)overset(20)sum k (1)/(2^(k)) is equal to

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  16. Let the sum of the first n terms of a non-constant A.P., a(1), a(2), a...

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  18. The sum of the the series 1+2x3+3x5+4x7+…. Upto 11^(th) term is

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  19. If the sum and product of the first three terms in an AP are 33 and 11...

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  20. Let S=3+(5(a^(3)+2^(3)))/(1^(2)+2^(2))+(7(1^(3)+2^(3)+3^(3)))/(1^(2)+2...

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