Find the value of (1.02)6, correct upto four places of decimal - Mathematics and Statistics

Sum

Find the value of (1.02)⁶, correct upto four places of decimal

(1.02)⁶ = (1 + 0.02)⁶

= ⁶C₀(1)⁶(0.02)⁰ + ⁶C₁(1)⁵(0.02)¹ + ⁶C₂(1)⁴(0.02)² + ⁶C₃(1)³(0.02)³ + ⁶C₄(1)²(0.02)⁴ + ⁶C₅(1)¹(0.02)⁵ + ⁶C₆(1)⁰(0.02)⁶

Since, ⁶C₀ = ⁶C₆ = 1, ⁶C₁ = ⁶C₅ = 6,

⁶C₂ = ⁶C₄ = `(6 xx 5)/(2 xx 1)` = 15, ⁶C₃ = `(6 xx 5 xx 4)/(3 xx 2 xx 1)` = 20

∴ (1.02)⁶ = 1(1)(1) + 6(1)(0.02) + 15(1)(0.0004) + 20(1)(0.000008) + ……

= 1 + 0.12 + 0.0060 + 0.000160 + ……

= 1.12616

= 1.1262, correct upto 4 decimal places.

Concept: Binomial Theorem for Positive Integral Index

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Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.2 | Q 8 | Page 77