JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Let

f(1)=1

, and

f(n)=2 \sum\limits_{{r=1}}^{n-1} f(r)

. Then

\sum\limits_{{r=1}}^m f(r)

is equal to:

View answer and explanation

Correct option: C

3^{m-1}

Option C is correct. By recursively applying the given formula

f(n)=2 \sum\limits_{{r=1}}^{n-1} f(r)

and simplifying, we can find that

\sum\limits_{{r=1}}^m f(r) = 3^{m-1}

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