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

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

대답:

#1#

설명:

첫 번째 유의 사항:

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

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

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

그래서:

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

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

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

#=13-12#

#=1#