Answer:
[tex]1+2+3+4+=4\times \frac{5}{2}\\ 1+2+3+4+5=5 \times \frac{6}{2}[/tex]
Step-by-step explanation:
The given equation are
[tex]1=1\times \frac{2}{2} \\1+2=2\times \frac{3}{2}\\ 1+2+3=3\times \frac{4}{2}\\ 1+2+3+?=?\times \frac{?}{?}\\ 1+2+3+?+?=?\times \frac{?}{?}[/tex]
As you can observe, the left side of equation has a sum which increases by one. The right side of the equation has a product between a number and a fraction, the number increases 1 unit, and the numerator of the fraction also increases 1 unit, but the denominator remains the same.
Applying this patterns, the third and fourth equation are
[tex]1+2+3+4+=4\times \frac{5}{2}\\ 1+2+3+4+5=5 \times \frac{6}{2}[/tex]
Therefore, the two last equation completed are
[tex]1+2+3+4+=4\times \frac{5}{2}\\ 1+2+3+4+5=5 \times \frac{6}{2}[/tex]
