Question: Consider the sequence n defined by Evaluate 64 and 128 (without using the y x key of your calculator), and use extrapolation

Consider the sequence Φ_n defined by

on x = [(+9 + (-9] n Show that e as no. Using the power series expansions of In(1+x) and e, show that (1 +

Evaluate Φ₆₄ and Φ₁₂₈ (without using the y^x key of your calculator), and use extrapolation to estimate the value of e.

on x = [(+9 + (-9] n Show that , e as no. Using the power series expansions of ln(1 +x) and e, show that (1 + )" = exp[n in (1 + )] n 1 11 + 2n 24n = c(1-7 and deduce that 11 $ = 0 (1 +241 +...) 71 24n 7 16 +

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