7. Correct
- - -
9. By the ratio test, the series will converge if
The limit reduces to
where
because
is given. So the series converges when
This means the radius of convergence is
.
- - -
10. By the ratio test, the series converges if
The limit is
and so the radius of convergence is 1.
- - -
11. Incorrect. By the root test, the series converges for
which means the series converges for all
, and so the interval of convergence is
.
- - -
For 14 and 16, it'll probably be too late to edit this post by the time you see this. You can try posting the remaining problems in a new question.
<em><u>Observe the pattern it follows:</u></em>
7....10....16......28
3. 6. 12
<em><u>The</u></em><em><u> </u></em><em><u>numbers</u></em><em><u> </u></em><em><u>added</u></em><em><u> </u></em><em><u>each</u></em><em><u> </u></em><em><u>time</u></em><em><u> </u></em><em><u>are</u></em><em><u> </u></em><em><u>doubled</u></em><em><u> </u></em><em><u>as</u></em><em><u> </u></em><em><u>you</u></em><em><u> </u></em><em><u>can</u></em><em><u> </u></em><em><u>see</u></em><em><u>.</u></em>
<em><u>therefore</u></em><em><u>:</u></em>
<em><u>7</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>1</u></em><em><u>0</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>1</u></em><em><u>6</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>2</u></em><em><u>8</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>5</u></em><em><u>2</u></em>
<em><u> </u></em><em><u> </u></em><em><u> </u></em><em><u> </u></em><em><u> </u></em>3. 6. 12. 24
<em><u>Hope</u></em><em><u> </u></em><em><u>that</u></em><em><u> </u></em><em><u>helped</u></em><em><u> </u></em><em><u>you</u></em><em><u>!</u></em>
Answer:
11/12 is greater than 1/2.
Step-by-step explanation:
We can make them have a common denominator of 12 to compare:
11/12 = 11/12
1/2 = 6/12.
So from this, we can see that 11/12 > 6/12.
___________________________
◆ AREA RELATED TO CIRCLES ◆ ___________________________
As shown in the figure ,
Radius of circle = 5 cm
Side of square = 2 × (Radius of inscribed circle)
Side of square = 2 × 5 cm
Side of square = 10 cm = a
___________________________
Now ,
Area of shaded region = (Area of square) - ( Area of inscribed circle )
Area of shaded region =
Area of shaded region =
Area of shaded region = 100 - 78.571
42
let the smallest even number be x, than the four even numbers are x, x+2, x+4, x+6, their sum is 180
x+x+2+x+4+x+6=180
4x+12=180
4x=168
x=42
the smallest even number is 42.