Question

Please help I will fan and medal!!!

0.30+0.31+0.32+0.33+0.34+....0.47+0.48+0.49+0.50

Answer 1

you could write each term as
0.30+ x
where x is 0.00 0.01, 0.02, etc
you have 21 terms
so you have
0.30*21 + 1/100 * sum 0,1,2,3,... 20
the what is the sum of the integers from 1 to 20 ? (there is a formula for this) ?

Answer 2

its ok i figured it out from there

Answer 3

for example, if we do just the first 3 terms, we would write it like this
0.3 + 0 + 0.3 + 0.01 + 0.3 + 0.02
when adding we can reorder , right ? so we could write this as
0.3 + 0.3 + 0.3 + 0 + 0.01 + 0.02
we have add 0.3 three times. in other words we can write that as
0.3 * 3 + 0 + 0.01 +0.02

now look at 0+0.01+0.02
we could (to make it look like whole numbers)
multiply and divide each by 100:
\[0.00 \cdot \frac{100}{100} +0 .01 \cdot \frac{100}{100} +0.02\cdot \frac{100}{100} \]
which is the same as
\[ \frac{0}{100} + \frac{1}{100} +\frac{2}{100} \\
\frac{1}{100} \left( 0+1+2\right)\]
and we have
\[ 0.3 \cdot 3 + \frac{1}{100} \sum_{n=0}^3n \]