Find the sum of 50 terms of the sequence:- .7 + .77 + .777 + .7777 + ................... ....
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Answered by
3
~Sn= n/2[2a+(n-1)d
~S50= 50/2 [2(0.7)+(50-1)0.07]
~S50=25[1.4+49×0.07]
~S50=25(4.83)
~S50=120.75
Answered by
4
0.7+0.77+0.777 .............
=7(0.1+0.11+0.111........)
=7/9(0.9+0.99+0.99.....to nth term)
=7/9(1-1/10+1-1/100+1-1000......to nth term)
=7/9[(1+1+1 to nth term) - (1/10+1/100+1/1000.......)
=7/9[n-[1/10(1-10^n)/1-1/10]
=7/9(n-(1-1/10^n)*1/9]
=7/81[n-(1-1/10^n)
For 50 terms
n=50
=7/81(50-(1-1/10^50)
=7/81[50-(1-1/10^50]
=4.2309-1-1/10^50
=3.23×10^50-1/10^50
=7(0.1+0.11+0.111........)
=7/9(0.9+0.99+0.99.....to nth term)
=7/9(1-1/10+1-1/100+1-1000......to nth term)
=7/9[(1+1+1 to nth term) - (1/10+1/100+1/1000.......)
=7/9[n-[1/10(1-10^n)/1-1/10]
=7/9(n-(1-1/10^n)*1/9]
=7/81[n-(1-1/10^n)
For 50 terms
n=50
=7/81(50-(1-1/10^50)
=7/81[50-(1-1/10^50]
=4.2309-1-1/10^50
=3.23×10^50-1/10^50
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