Sequence And Series Question 637
Question: The product (32)(32) 1/6(32)1/36 …… to $ \infty $ is
[Kerala (Engg.) 2005]
Options:
A) 16
B) 32
C) 64
D) 0
E) 62
Show Answer
Answer:
Correct Answer: C
Solution:
(32)(32)1/6(32)1/36…… $ \infty $ = $ {{(32)}^{1+\frac{1}{6}+\frac{1}{36}+…..\infty }} $ $ ={{(32)}^{\frac{1}{1-(1/6)}}} $ $ ={{(32)}^{\frac{1}{5/6}}}={{(32)}^{6/5}} $ $ =2^{6}=64 $ .
BETA
