计算:a+(a+b)+(a+2b)+(a+3b)+.+(a+99b)请详细解答,

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计算:a+(a+b)+(a+2b)+(a+3b)+.+(a+99b)请详细解答,

计算:a+(a+b)+(a+2b)+(a+3b)+.+(a+99b)请详细解答,
计算:a+(a+b)+(a+2b)+(a+3b)+.+(a+99b)请详细解答,

计算:a+(a+b)+(a+2b)+(a+3b)+.+(a+99b)请详细解答,
答:
a+(a+b)+(a+2b)+(a+3b)+.+(a+99b)
=a+a+...+a+(b+2b+3b+...+99b) (100个a相加,99项b的单项式相加)
=100a+(b+99b)*99/2
=100a+50*99b
=100a+4950b

原式=100a+(1+2+3+4+……+99)b=100a+4950b

=100a+(0b+b+2b+3b+……+99b)
=100a+[(0b+99b)+(b+98b)+(2b+97b)+……+(49b+50)]
=100a+49X99b
=100a+4851b