Question

計(jì)算：0.2+0.4+…+0.8+0.10+0.12+…+0.98+0.100=

26.4

．

Answer 1

分析：是一個(gè)等差數(shù)列的問(wèn)題，根據(jù)公式：和=（首項(xiàng)+末項(xiàng)）×項(xiàng)數(shù)÷2，項(xiàng)數(shù)的求法：項(xiàng)數(shù)=（末項(xiàng)-首項(xiàng)）÷公差+1；此題分為兩個(gè)等差數(shù)列，0.2+0.4+…+0.8和0.10+0.12+…+0.98+0.100，前一個(gè)數(shù)列的公差是0.2，后一個(gè)數(shù)列的公差就是0.02，據(jù)此解答．

解答：解：0.2+0.4+…+0.8+0.10+0.12+…+0.98+0.100，
=（0.2+0.8）×[（0.8-0.2）÷0.2+1]÷2+（0.10+0.98）×[（0.98-0.10）÷0.02+1]÷2+0.100，
=2+24.3+0.1，
=26.4．
故答案為：26.4．

點(diǎn)評(píng)：此題運(yùn)用了高斯求和公式進(jìn)行解答，關(guān)鍵是確定項(xiàng)數(shù)和公差．