Question

Which term of the series 2+1/✓2+1/4+......is 1/32

Answer 1

Answer:

5

Step-by-step explanation:

a1 = 2

a2 = 1/\sqrt{2}

r(common ratio) = a2/a1

1/\sqrt{2}/2 = 1/2\sqrt{2}

a*r^{n-1} = 1/32

2(1/2\sqrt{2} )^{n-1} = 1/32

(1/2\sqrt{2} )^{n-1} =1/64

(2\sqrt{2} )^{n-1} =64

2^{n-1} * 2^{(1/2)*n-1} = 2^{6}

2^{(2n-2+n-1)/2} = 2^{6}

2^{(3n-3)/2} = 2^{6}

bases are same so powers should be equal

(3n-3)/2 = 6

3n-3 = 12

3n = 15

n = 15/3

n= 5