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

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

⭐⭐

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b