If $\sum_{r=1}^n r^4=f(n)$, then $\sum_{r=1}^n(2 r-1)^4$ is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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\sum_{r=1}^n r^4=f(n)

, then

\sum_{r=1}^n(2 r-1)^4

is equal to

View answer and explanation

Correct option: A

f(2 n)-16 f(n)

Option A (

f(2 n)-16 f(n)

) is correct because the sum of (2r-1)⁴ from r=1 to n can be expressed as the difference between the sum of r⁴ from r=1 to 2n and 16 times the sum of r⁴ from r=1 to n.

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(ii)

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(iii)

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\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

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