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 C392 f(x)=5x5x+5⋯(i) ⇒f(2−x)=52−x52−x+5 ⇒f(2−x)=55x+5⋯(ii)
Adding equation (i) and (ii) f(x)+f(2−x)=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