Use the integral test to determine if the series is convergent or divergent.

Convergent

Step-by-step explanation:

∑₁°° n / (n² + 1)²

Applying integral test:

∫₁°° x / (x² + 1)² dx

If u = x² + 1, then du = 2x dx, or ½ du = x dx.

When x = 1, u = 2.  When x = ∞, u = ∞.

½ ∫₂°° 1 / u² du

½ (-1 / u) |₂°°

½ (-1 / ∞) − ½ (-1 / 2)

0 + ¼

¼

The integral converges, so the series also converges.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

just sum

10 + 10 = 20