Question

已知数列lg2,lg4,lg8,lg16,...的前n项和等于55lg2,则n等于多少?

Answer 1

lg2+lg4+lg8+lg16+……lg2^n=55lg2

lg2+2lg2+3lg2+4lg2+……+nlg2=55lg2(根据log(a)(M^n)=nlog(a)(M))

1+2+3+4+……+n=55

n+n(n-1)/2=55

n=-11或n=10(n>0)

n=10