4 ki power 1/2 +4 ki power 1/4+ 4 ki power 1/8+...........infinite term ? give me answer plz

Question

4^1/2 + 4^1/4 4^1/8 +4^1/16 +..............infinite term? find sum of terms?

Answer 1

it appears to be an infinite series (although you omitted a key + sign after 4 to the ¼.

 

first term is 2 (square root of 4)

general term is 4^p where p = 1/2ⁿ and n is the term number.

 

as n goes to infinity, p goes to 0 and so the individual terms approach 1.

 

Such an infinite series with no term < 1 does not converge. Sum is infinite.

Answer 2

If you keep making the exponent smaller, the terms get closer to zero.  However, the largest term in the sequence is 2.  Therefore, the sum converges to 2.