# Use the table in the picture to you find a Function with the indicated series representation. Transcribed Image Text: Table 11.5 = 1 + x

Use the table in the picture to you find a Function with the indicated series representation. Transcribed Image Text: Table 11.5
= 1 + x + x² +.. +x* + . ..
1 – x
Σ, for lx <1 %3D =1- x + x² - (-1)** + = (-1)*x*, for |x| < 1 %3D 1 + x et = 1 + x + 2! for |x| < ∞ %3D k! k!' (-1)*x2k+1 (2k + 1)! (-1)*x2*+1 (2k + 1)! ' sin x = x - 3! for |x < 0 1. t 5! k=0 .2k (-1)*x* (-1)* x²* cos x = 1 - 2! for x < ∞ 4! (2k)! (2k)! k=0 x² In (1 + x) = x - (-1)*+1 x* (-1)*+1,k for -1 < x S< 1 3 k=1 x² -In (1 – x) = x + .3 + · k for -1 < x < 1 k=1 (-1)*x2%+1 (-1)* x2*+1 8. tanx = x - 3. for |x s 1 2k + 1 2k + 1 k=0 2k 2k +1 sinh x = x + 3! +...+ 5! for x < ∞ (2k+1)! k=0(2k + 1)!" x² cosh x = 1 + 2! 2k Σ (2k)!" for x < ∞ +. %3D 4! (2k)! E. for lal < 1 and (P) - Pp - Dp - 2) (P – k + 1) (P) - 1 p(p 1)(p - 2)-- (p – k + 1) (.) (1 + x) = , for x< 1 and %3D 3D1 k! 8. 8. 8. 8. 8. || 8. || 8. Transcribed Image Text: 8x 2x 32x 128x +. +... 3.