Suppose that P[infinity] n=0 cnx n converges when x = −5 and diverges when x = 7. What can be said about the convergence or divergence of the following series? (a) X[infinity] n=0 cn

What can be said about the convergence or divergence of the following series? summation n=0 to infinite (-1)^n Cn9^n

The series diverges

Step-by-step explanation:

Given.

The center of convergence of the series, ΣCnx^n = 0 (for n = 0 to ∞)

The interval of the convergence is of the form (-k,k)

One or both the end points may be included in the intervals of convergence.

Also, given that the series diverges when x = 7; this implies that the interval of convergence is smaller than {-7,7}

The series

Σ(-1)^n Cn9^n (for n = 0 to ∞)

= Σ Cn(-9)^n (for n = 0 to ∞)

This is obtained after substituting -9 for x in ΣCnx^n = 0

So, x = -9

This is outside the boundary {-7,7}.

Hence, the given series diverges

The sum of Supplementary angle =180 degrees

(2x+3)⁰ +(3x+2)⁰=180⁰

adding like terms

5x+5=180

5x=180-5

5x=175

x=175/5 =35 degrees

so the two angles are :

(2x+3)⁰ =2*35 +3 = 73⁰

(3x+2)⁰=3*35 +2 =105+2 = 107⁰

so correct option is D , 73⁰ and 107⁰