Simplificați expresia ?: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / sqrt (168) + sqrt

Răspuns:

#1#

Explicaţie:

Prima observație că:

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

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

#color (alb) (1 / (sqrt (n + 1) + sqrt (n))) = sqrt (n + 1)

Asa de:

# 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#