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2015-03-07T21:45:58+05:30

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USE THIS G.P EQUATION
a+ar+ar^2+..+ar^{n-1}= \frac{a(r^n-1)}{r-1}

if r<1
a+ar+ar^2+..+ar^{n-1}= \frac{a(1-r^n)}{1-r}

first one:

1+ \frac{1}{2}+ \frac{1}{4}+..+\frac{1}{2^8}= \frac{1- \frac{1}{2^9}}{1- \frac{1}{2}}=511/(2^8)=1.99609375

second one:

30+3+ \frac{3}{10}+ \frac{3}{100}+..+\frac{3}{10^6}=3[10+1+ \frac{1}{10}+ \frac{1}{100}+..+\frac{1}{10^6}]
=3\frac{10[1- \frac{1}{10^{8}}]}{1- \frac{1}{10}}= \frac{30(10^8-1)}{9(10^7)}=33.333333

third one:
10,000+1,000+100+10+,,,,,,,+ \frac{1}{10,000}= \frac{10000(1- \frac{1}{10^9} )}{1-\frac{1}{10}} =11111.1111

fourth one:
1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+..+-\frac{1}{2^8}=1+[-\frac{1}{2}]+[-\frac{1}{2}]^2+[-\frac{1}{2}]^3+..+[-\frac{1}{2}]^8=
\frac{1-[-\frac{1}{2}]^9}{1-[-\frac{1}{2}]}=0.66796875


3 5 3
hiiiiii
first and second are wrong.
correct them
done
thanks!