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Question

A function f(x) is given by f(x)=5x5x+5, then the sum of the series f(120)+f(220)+f(320)+.....+f(3920) is equal to:

A
192
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B
492
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C
392
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D
292
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Solution

The correct option is C 392
f(x)=5x5x+5(i)
f(2x)=52x52x+5
f(2x)=55x+5(ii)
Adding equation (i) and (ii)
f(x)+f(2x)=1
f(120)+f(3920)=1
f(220)+f(3820)=1
:
:
f(1920)+f(2120)=1
and f(2020)=f(1)=12
(12)+f(220)+f(320)+....+f(3920)=19+12=392

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