WebCalculus. Calculus questions and answers. Which of the following is t he Maclaurin expansion of the function f (x) = x^2 cos (3x)? A) Sigma^infinity_n=0 (-1)^n 3^n/ (2n)! … WebApr 13, 2024 · If \\( x <1 \\), then in the expansion of \\( \\left(1+2 x+3 x^{2}+4 x^{3}+\\ldots\\right)^{1 / 2} \\), the coefficient \\( x^{n} \\), is:📲PW App Link - https
The coefficient of \( x^{x} \) in the expansion of \( 1+(1+x)+(1+x ...
WebNov 11, 2024 · 1/(1-x)^2 = sum_(n=0)^oo (n+1)x^n converging for absx < 1 Start from the geometric series: sum_(n=0)^oo x^n = 1/(1-x) converging for abs(x) < 1. Note now that: … WebApr 12, 2024 · If the coefficients of three consecutive terms in the expansion of (1 + x) n are in the ratio 1 : 5 : 20, then the coefficient of the fourth term of the expansion is (1) 3654 (2) 3658 (3) 3600 (4) 1000. jee main 2024; Share It On Facebook Twitter Email. 1 Answer +1 vote . answered 1 day ... homes for sale in mclouth kansas
The definition of e by limits of $(1+1/n)^n$ through series …
Web4. Binomial Expansions 4.1. Pascal's riTangle The expansion of (a+x)2 is (a+x)2 = a2 +2ax+x2 Hence, (a+x)3 = (a+x)(a+x)2 = (a+x)(a2 +2ax+x2) = a3 +(1+2)a 2x+(2+1)ax +x 3= a3 +3a2x+3ax2 +x urther,F (a+x)4 = (a+x)(a+x)4 = (a+x)(a3 +3a2x+3ax2 +x3) = a4 +(1+3)a3x+(3+3)a2x2 +(3+1)ax3 +x4 = a4 +4a3x+6a2x2 +4ax3 +x4. In general we see … WebMar 1, 2024 · How do you use the Binomial Theorem to expand (1 + x)−1? Precalculus The Binomial Theorem The Binomial Theorem 1 Answer Narad T. Mar 2, 2024 The answer is … WebDec 10, 2015 · sente. Dec 10, 2015. Assuming n is a nonnegative integer, then the binomial theorem states that. (a +b)n = n ∑ k=0C(n,k)an−kbk = n ∑ k=0 n! k!(n −k)! an−kbk. … hipster smiley face