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

The sum of the series: `1/((log)_2 4)+1/((log)_4 4)+1/((log)_8 4)++1/((log)_(2n)4)` is `(n(n+1))/2` (b) `(n(n+1)(2n+1))/(12)` (c) `(n(n+1))/4` (d) none of these

A

`(n (n + 1))/(2)`

B

`(n (n + 1) (2n + 1))/(12)`

C

`(1)/(n (n + 1))`

D

`(n (n + 1))/(4)`

Text Solution

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The correct Answer is:
D
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 4 (MULTIPLE CHOICE QUESTIONS)
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  2. Sum of n terms the series : 1^2-2^2+3^2-4^2+5^2-6^2+

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

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  4. The sum of the series (1)/(3 xx 7) + (1)/(7 xx 11) + (1)/(11 xx 15)+… ...

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  5. If (1^2-t1)+(2^2-t2)++(n^2-tn)+=(n(n^2-1))/3 , then tn is equal to n^2...

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  6. The sum of n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+.... is...

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  7. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

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  8. The sum of all the products of the first n(+) ive integers taken two a...

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  9. The value of the expression (1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+...

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  10. The value of the expression 2 (1 + omega) (1 + omega^(2)) + 3(2 omega ...

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  11. The value of the expression 1.(2-omega).(2-omega^2)+2.(3-omega)(3-omeg...

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  12. For and odd integer n ge 1, n^(3) - (n - 1)^(3) + …… + (- 1)^(n-1) ...

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  13. The sum of the series (1)/(3.5) + (1)/(5.7) + (1)/(7.9)+…. ad infinity...

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  14. If Sigma(r=1)^(n)t(r)=(1)/(6)n(n+1)(n+2), AA n ge 1, then the value o...

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  15. The sum of the infinite series 1 + (1+a) x + (1 + a + a^(2)) x^(2) + (...

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  16. Sum of the series 1 + 2 + 4 + 7 +…+ 67 is equal to

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  17. 99^(th) term of the series 2 + 7 + 14 + 23 + 34 +…is

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  18. Find the 50th term of the series 2+3+6+11+18+….

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  19. Let P = 3^(1//3). 3^(2//9) . 3^(3//27)…oo, then P^(1//3) is equal to

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  20. 2^(1//4).4^(1//8).8^(1//16).16^(1//32)…. is equal to

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