Evaluate $$0.30+0.31+0.32+0.33+0.34+\cdots+0.47+0.48+0.49+0.50.$$express - id030031032033034047044124748, trippynarco

Ответ:

dpranavesh446

12.01.2022

$S_{21}=8.4$

Step-by-step explanation:

Sum Of Arithmetic Sequences

Given a sequence

a_1, a_1+r, a_1+2r, ...., a_1+(n-1)r

The sum of all terms is

$\displaystyle S_n=n\frac{a_1+a_n}{2}$

a_n=a_1+(n-1)r

If we know a_n, a_1, r

we can compute n as

$\displaystyle n=\frac{a_n-a_1}{r}+1$

The given sequence is

0.30+0.31+0.32+...+0.50

The common difference is

r=0.31-0.30=0.01

a_1=0.30, a_n=0.50

We compute n

$\displaystyle n=\frac{0.50-0.30}{0.01}+1$

n=21

So the given sum is

$\displaystyle S_{21}=21\frac{0.30+0.50}{2}$

$S_{21}=21(0.40)$

$S_{21}=8.4$

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