Q6. (1) Given log(1+t) = t = t + t² 4 valid for 1411, determine the power. series for log (1+2x) up to powers of and write down the radius of convergence, t 2 3 11/ Given e² = 1+t+t² +² +-n, valid for all t t 2! 3! 2 = 1+t+t²rt³ron, valid for 161 <1, 3 and 1-t 3 Show 2* = 1-2x + x²-12 X² + --- 17 4 24 1 + 2/1/2012

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A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

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A:

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A: For the given alternate series, to find the partial sum and error bound for it.

Q: Substitute x 2 for x in the Maclaurin series for sin x.

A: To Substitute x2 for x in the Maclaurin series for sin x

Q: CONVERGENT

A: We have to choose the correct option from the given options according to the given information

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A: