The infinite series s(x) = 1 - tan²(x) + tan⁴(x) - tan⁶(x) converges for 0 < x < π/4. The derivative of this series, s'(x), can be derived by first recognizing it as a geometric series. The correct approach involves summing the geometric series and differentiating the result, leading to the conclusion that s'(x) = -tan²(x). This matches option C from the provided answers.
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cj5892 said:Homework Statement
Consider the infinite series s(x)=1-tan^2(x)+tan^4(x)-tan^6(x)+... , where 0<x<pi/4
s'(x)=
A.sin2x
B.cos2x
C.-tan2x
D.-sin2x
E.-cos2xThe Attempt at a Solution
Attempting to derive the series, i get 1-2tanxsec^2x+4tan^3(x)sec^2(x)-6tan^5(x)sec^2(x)+...
am i missing something obvious here? i don't see any trig identities in that that would give any of the answers
cj5892 said:i still can't get it :(