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calculati suma numerelor a=1+1/2+1/3+1/4+..............+1/100 b=1/2+2/3+3/4+...................+99/100

Răspuns :

a+b=1 +1/2+1/3+1/4+..+1/100+1/2+2/3+3/4+..+99/100
a+b=1+1/2+12+1/3+2/3+1/4+3/4+...+1/100+99/100
a+b=1+2/2+3/3+4/4+...+100/100
=(1+1+1+...+1)de 100de ori
rezultă:
a+b=100