Question
Question: If H<sub>n</sub> = 1 + \(\frac{1}{2}\) + …. + \(\frac{1}{n}\)then the value of 1 + \(\frac{3}{2}\) +...
If Hn = 1 + 21 + …. + n1then the value of 1 + 23 + 35 + …. + n2n−1 is –
A
Hn + n
B
2n – Hn
C
(n – 1) + Hn
D
Hn + 2n
Answer
2n – Hn
Explanation
Solution
1 + 23 + 25+….+n2n−1
= (2 – 1) + (2 – 1/2) + (2 – 1/3) + ….. + (2 – 1/n)
= 2n – Hn.