Question

用數(shù)學(xué)歸納法證明:++…+= (n∈N*).

 

Answer 1

見(jiàn)解析

【解析】①當(dāng)n=1時(shí),左邊==,右邊==,

左邊=右邊,等式成立;

②假設(shè)n=k(k≥1,k∈N*)時(shí),等式成立,

即++…+=,

當(dāng)n=k+1時(shí),左邊

=++…+

+

=+

=

=

=,

所以當(dāng)n=k+1時(shí),等式成立.

由①②可得對(duì)任意n∈N*,等式成立.