Question

For a positive integer n, let a(n) = 1 + $\frac { 1 } { 3 }$+$\frac { 1 } { 4 }$ + ……+ $\frac { 1 } { \left( 2 ^ { \mathrm { n } } \right) - 1 }$ . Then

• A. a (100) < 100
• B. a (100) > 100
• C. a (200) < 100
• D. None of these

Answer 1

Answer: (A)

a (100) < 100

Answer 2

We have

a(n)=1+$\frac { 8 } { 8 }$ + ….. + $\frac { 2 ^ { n - 1 } } { 2 ^ { n - 1 } }$ = nThus, a(100) < 100