ลดความซับซ้อนของนิพจน์: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169))

ลดความซับซ้อนของนิพจน์: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169))
Anonim

ตอบ:

#1#

คำอธิบาย:

ทราบก่อนว่า:

# 1 / (sqrt (n + 1) + sqrt (n)) = (sqrt (n + 1) -sqrt (n)) / ((sqrt (n + 1) + sqrt (n)) (sqrt (n + 1) -sqrt (n)) #

#color (white) (1 / (sqrt (n + 1) + sqrt (n))) = (sqrt (n + 1) -sqrt (n)) / ((n + 1) -n) #

#color (white) (1 / (sqrt (n + 1) + sqrt (n))) = sqrt (n + 1) -sqrt (n) #

ดังนั้น:

# 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + … + 1 / (sqrt (168) + sqrt (169)) #

# = (sqrt (145) -sqrt (144)) + (sqrt (146) -sqrt (145)) + … + (sqrt (169) -sqrt (168)) #

# = sqrt (169) -sqrt (144) #

#=13-12#

#=1#