How many 147

What is the minimum number of consecutive natural numbers from 1 to n that must be added so that their sum exceeds 1,000,000?

Final Answer:

n =  1414

Step-by-step explanation:

s=1000000 a1=1 d=1  sn =2a1+an n sn =2a1+a1+(n1) d n  2s=(2 a1+(n1)) n  2 1000000=(2 1+(n1)) n n2n+2000000=0 n2+n2000000=0  a=1;b=1;c=2000000 D=b24ac=1241(2000000)=8000001 D>0  n1,2=2ab±D=21±8000001=21±3888889 n1,2=0.5±1414.213651 n1=1413.713650761 n2=1414.713650761  n=n1=1413.7137=1414   Verifying Solution:   an=a1+(n1) d=1+(14141) 1=1414  s2=2a1+an n=21+1414 1414=1000405

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