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1.3+3.5+5.7+.................+97.99
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\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{1}{3}+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{97}-\frac{1}{97}\right)-\frac{1}{99}\)
\(=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)
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A = 1.3 +3.5 + 5.7 + ...+ 97.99
6A= 1.3.6 + 3.5.6 + 5.7.6 + ... + 97.99.6
= 1.3.(5+1) + 3.5.(7-) + 5.7(9-3) + ... + 97.99(101-95)
= 1.3.5 + 1.3 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ... + 97.99.101 - 95.97.99
= 1.3.5 + 3 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + .... + 97 .99.101 - 95.87.99
=3+97.99.101
=> A = ( 1+97.33.101) : 2
A= 161651
\(S=4\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=4\cdot\left(\dfrac{1}{3}-\dfrac{1}{99}\right)=4\cdot\dfrac{32}{99}=\dfrac{128}{99}\)
S=4(13−15+15−17+...+197−199)S=4(13−15+15−17+...+197−199)
=4⋅(13−199)
=4⋅3299=12899
2/3.5+ 2 /5.7+ 2/7.9+...+ 2/97.99
=1/3-1/5+1/5-1/7+1/7-1/9+....+1/97-1/99
=1/3-1/99
=32/99
2/3.5 + 2/5.7 +...+ 2/97.99
=1/3 - 1/5 + 1/5 - 1/7 + ... + 1/97 - 1/99
=1/3 - 1/99
=32/99
= 2/ 3.5 = 1/3 - 1/5 ; 2/ 5.7 = 1/5 - 1/7 ;........; 2/ 97.99 = 1/97 - 1/99
= 1/3 - 1/99 = 32/99
= \(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{97}-\dfrac{1}{99}\)
\(=\dfrac{1}{3}-\dfrac{1}{99}=\dfrac{32}{99}\)