Question

Find the value of e³ using first 5 terms of the expansion of eˣ.

Answer 1

we know by the concept of expansion,

expansion of $e^x$ = 1 + x + x²/2! + x³/3! + x⁴/4! + ......

we have to find value of e³ using first 5 terms.

e.g., e³ = 1 + 3 + 3²/2! + 3³/3! + 3⁴/4!

= 1 + 3 + 9/2 + 27/6 + 81/24

= 131/8

= 16.375

hence, value of e³ = 16.375