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Question: If H<sub>n</sub> = 1 + \(\frac{1}{2}\) + …. + \(\frac{1}{n}\)then the value of 1 + \(\frac{3}{2}\) +...

If Hn = 1 + 12\frac{1}{2} + …. + 1n\frac{1}{n}then the value of 1 + 32\frac{3}{2} + 53\frac{5}{3} + …. + 2n1n\frac{2n - 1}{n} is –

A

Hn + n

B

2n – Hn

C

(n – 1) + Hn

D

Hn + 2n

Answer

2n – Hn

Explanation

Solution

1 + 32\frac{3}{2} + 52\frac{5}{2}+….+2n1n\frac{2n - 1}{n}

= (2 – 1) + (2 – 1/2) + (2 – 1/3) + ….. + (2 – 1/n)

= 2n – Hn.