Question

Which of the following is the correct expanded form for the series below?

Answer 1

The first one is correct

Explanation:

simply plug in numbers from 0 to 4 in the position of n, which, in this case is -2^n.

the form comes out to:

-2^0, -2^1, -2^2, -2^3, -2^4

notice how the exponent does not include the negative, so it always remains negative. The one you selected would have been correct if it was (-2)^n

Answer 2

the correct answer is option B

Explanation:

given ,

`\sum_(n= 0)^(4)-2^n`

for the series expansion we have to put the value in the function one by one

by putting value n = 0 the value -2ⁿ = -2⁰ comes out to be 1

by putting value n = 1 the value -2¹ = -2 comes out to be -2

by putting value n = 2 the value -2² = 4 comes out to be 4

by putting value n = 3 the value -2³ = -8 comes out to be -8

by putting value n = 4 the value -2⁴ = 16 comes out to be 16

hence, the series formed is

= 1 - 2 + 4 - 8 + 16

the correct answer is option B