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           ☆算术计算1题

〖1/1算式〗
    作业:求算式 3/(1+5%)^30+3/(1+5%)^31+3/(1+5%)^32+3/(1+5%)^33+3/(1+5%)^34+3/(1+5%)^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40 的值.
    题型:数学计算
    解:
          3/(1+5%)^30+3/(1+5%)^31+3/(1+5%)^32+3/(1+5%)^33+3/(1+5%)^34+3/(1+5%)^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/(1+5%)^31+3/(1+5%)^32+3/(1+5%)^33+3/(1+5%)^34+3/(1+5%)^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/(1+5%)^32+3/(1+5%)^33+3/(1+5%)^34+3/(1+5%)^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/(1+5%)^33+3/(1+5%)^34+3/(1+5%)^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/1.05^33+3/(1+5%)^34+3/(1+5%)^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/1.05^33+3/1.05^34+3/(1+5%)^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/1.05^33+3/1.05^34+3/1.05^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/1.05^33+3/1.05^34+3/1.05^35+3/1.05^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/1.05^33+3/1.05^34+3/1.05^35+3/1.05^36+3/1.05^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/1.05^33+3/1.05^34+3/1.05^35+3/1.05^36+3/1.05^37+3/1.05^38+3/(1+5%)^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/1.05^33+3/1.05^34+3/1.05^35+3/1.05^36+3/1.05^37+3/1.05^38+3/1.05^39+3/(1+5%)^40
        =3/1.05^30+3/1.05^31+3/1.05^32+3/1.05^33+3/1.05^34+3/1.05^35+3/1.05^36+3/1.05^37+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/1.05^31+3/1.05^32+3/1.05^33+3/1.05^34+3/1.05^35+3/1.05^36+3/1.05^37+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/1.05^32+3/1.05^33+3/1.05^34+3/1.05^35+3/1.05^36+3/1.05^37+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/1.05^33+3/1.05^34+3/1.05^35+3/1.05^36+3/1.05^37+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/1.05^34+3/1.05^35+3/1.05^36+3/1.05^37+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/1.05^35+3/1.05^36+3/1.05^37+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/1.05^36+3/1.05^37+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/1.05^37+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/1.05^38+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/1.05^39+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/1.05^40
        =3/4.321942375150668+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+3/4.538039493908201+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+3/4.764941468603611+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+0.629598+3/5.003188542033792+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+0.629598+0.599618+3/5.253347969135482+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+0.629598+0.599618+0.571064+3/5.516015367592257+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+0.629598+0.599618+0.571064+0.543871+3/5.791816135971869+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+0.629598+0.599618+0.571064+0.543871+0.517972+3/6.081406942770463+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+0.629598+0.599618+0.571064+0.543871+0.517972+0.493307+3/6.385477289908986+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+0.629598+0.599618+0.571064+0.543871+0.517972+0.493307+0.469816+3/6.704751154404436+3/7.039988712124658
        =0.694132+0.661078+0.629598+0.599618+0.571064+0.543871+0.517972+0.493307+0.469816+0.447444+3/7.039988712124658
        =0.694132+0.661078+0.629598+0.599618+0.571064+0.543871+0.517972+0.493307+0.469816+0.447444+0.426137
        =1.35521+0.629598+0.599618+0.571064+0.543871+0.517972+0.493307+0.469816+0.447444+0.426137
        =1.984808+0.599618+0.571064+0.543871+0.517972+0.493307+0.469816+0.447444+0.426137
        =2.584426+0.571064+0.543871+0.517972+0.493307+0.469816+0.447444+0.426137
        =3.15549+0.543871+0.517972+0.493307+0.469816+0.447444+0.426137
        =3.699361+0.517972+0.493307+0.469816+0.447444+0.426137
        =4.217333+0.493307+0.469816+0.447444+0.426137
        =4.71064+0.469816+0.447444+0.426137
        =5.180456+0.447444+0.426137
        =5.6279+0.426137
        =6.054037

    答案:3/(1+5%)^30+3/(1+5%)^31+3/(1+5%)^32+3/(1+5%)^33+3/(1+5%)^34+3/(1+5%)^35+3/(1+5%)^36+3/(1+5%)^37+3/(1+5%)^38+3/(1+5%)^39+3/(1+5%)^40=6.054037


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