Begin with the series solution y-? ~anz" to derive the recursive relation (n +2)(n +1)an+ -an-2, n2 2 for the differential equation y+2y0 and write out the first six non-zero terms.

I guess the ODE is supposed to be

So if

then

so that

for , or equivalently,

for . Note the dependency between every other coefficient - this means we can consider two cases:

and so on, with

and so on, with

Then the ODE has solution

and the first six non-zero terms occur for , for which we get

40. x = 106 degrees

41. x = 118 degrees

Step-by-step explanation:

40.

straight line has 180 degrees

180 - 128 = 52 : angle inside triangle

180 - 126 = 54 : angle inside triangle

52 + 54 = 106

triangle has 180 degrees

180 - 106 = 74 : 3rd angle inside the triangle

again straight line has 180 degrees

180 - 74 = 106 = x

41.

shape of 4 sides is 360 degrees

180 - 34 = 146

little box means one the sides is 90 degrees on either side

146 + 90 = 236

360 - 236 = 124

both x's are the same so angles inside are the same too

124 ÷ 2 = 62

straight line is 180

180 - 62 = 118

x = 118