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The value of $(1.1)^{10}$ correct to $4$ decimal places is

1. $2.4512$
2. $1.9547$
3. $2.5937$
4. $1.4512$

retagged | 53 views
0
I am getting 2.5910 by binomial theorem.

Using pascal triangle

We can see that that the 6th row is $1,5,{\color{Red} {10}},{\color{Blue} {10}},5,1$ so

$11^5 = 1(5+{\color{Red} 1})({\color{Red} 0}+{\color{Blue} {1}}){\color{Blue} {0}}51 = 161051$ $\implies (1.1)^5 = 1.61051$

$(1.1)^{10} = (1.1)^5*(1.1)^5 = 1.61051*1.61051 \approx 1.61*1.61 = 2.5921$

$\therefore$ Option $C.$ is the correct answer

by Boss (25.1k points)
0
$2.5937$ is given in the options?
0
No but option C is most appropriate.

+1 vote