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If ai > 0 for i = 1, 2, 3,..,n and a1, a2, a3, ...an = 1 then the greatest value of (1 + a1)(1 + a2)... (1 + an) is:
  • a)
    22n
  • b)
    2n
  • c)
    1
  • d)
    2n/2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If ai> 0 for i = 1, 2, 3,..,n and a1, a2, a3, ...an= 1 then the gre...
Let the given expansion be f(n)
f(n) = (1 + a1)(1 + a2)... (1 + an)
Also given, a1 = a2 = a3 = ... = an = 1
Consider for n = 2
f(2) = (1 + a1)(1 + a2)
f(2) = (1 + 1)(1 + 1) = 22
Consider for n = 5
f(5) = (1 + a1)(1 + a2)(1 + a3)(1 + a4)(1 + a5)
f(5) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1) = 25
Similary for n times, it is given as
f(n) = (1 + 1)(1 + 1) ...... (1 + 1) = 2n
(1 + a1)(1 + a2)... (1 + an) = 2n
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Most Upvoted Answer
If ai> 0 for i = 1, 2, 3,..,n and a1, a2, a3, ...an= 1 then the gre...
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