8c: use the binomial theorem to obtain the following series expansions1. [Hint: By the binomial theorem, (1+)-1+ 1 Extracted text: Chapte 434 1. (1+x)'/2 = 1 +* (c) 2. 2.4 1.3 x'+... 2.4.6 1.3.5...(2n – 3) + (-1)"+1 2.4.6...(2n) +……. .... 1 (1+x)-1/2 = 1- (d) +... 2.4 1-3.5...(2n – 1) +(-1)" x"+... 2.4.6...(2n) 9. Prove that the inequality 2 1. [Hint: By the binomial theorem, (1+)-1+ 1

Chapte 434 1. (1+x)'/2 = 1 +* (c) 2. 2.4 1.3 x'+... 2.4.6 1.3.5...(2n – 3) + (-1)"+1 2.4.6...(2n) +……. .... 1 (1+x)-1/2 = 1- (d) +... 2.4 1-3.5...(2n – 1) +(-1)" x"+... 2.4.6...(2n) 9. Prove that the...

8c: use the binomial theorem to obtain the following series expansions

Chapte<br>434<br>1.<br>(1+x)'/2 = 1 +*<br>(c)<br>2.<br>2.4<br>1.3<br>x'+...<br>2.4.6<br>1.3.5...(2n – 3)<br>+ (-1)

1. [Hint: By the binomial theorem, (1+)-1+ 1 < 1="" +1+="" 1="" +.="" 2.3="" 1="" +..="" 2.3.4...n="" 1="">< 1="" +="" 1.="" 1="" +...="" 22="" 1="" 2n-1*="" "/="">
Extracted text: Chapte 434 1. (1+x)'/2 = 1 +* (c) 2. 2.4 1.3 x'+... 2.4.6 1.3.5...(2n – 3) + (-1)"+1 2.4.6...(2n) +……. .... 1 (1+x)-1/2 = 1- (d) +... 2.4 1-3.5...(2n – 1) +(-1)" x"+... 2.4.6...(2n) 9. Prove that the inequality 2 < (1+="" 1/n)"="">< 3="" holds="" for="" all="" integers="" n=""> 1. [Hint: By the binomial theorem, (1+)-1+ 1 < 1="" +1+="" 1="" +.="" 2.3="" 1="" +..="" 2.3.4...n="" 1="">< 1="" +="" 1.="" 1="" +...="" 22="" 1="">

Jun 05, 2022

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Chapte 434 1. (1+x)'/2 = 1 +* (c) 2. 2.4 1.3 x'+... 2.4.6 1.3.5...(2n – 3) + (-1)"+1 2.4.6...(2n) +……. .... 1 (1+x)-1/2 = 1- (d) +... 2.4 1-3.5...(2n – 1) +(-1)" x"+... 2.4.6...(2n) 9. Prove that the...

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