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The value of (lim)(nvecoo)sum(r=1)^(r-1)...

The value of `(lim)_(nvecoo)sum_(r=1)^(r-1)(sum_(t=0)^(r-1)1/(5^n)dot^n C_rdot^r C_t .3^t)` is equal to

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The correct Answer is:
1
`underset(nrarroo)"lim"underset(r=1)overset(n)sum(1)/(5^(n))..^(n)C_(r)(underset(r=0)overset(r-1)sum.^(r)C_(t).3^(t))=underset(nrarroo)"lim"underset(r=1)overset(n)sum(1)/(5^(n))..^(n)C_(r)(4^(r)-3^(r))`
`= underset(nrarroo)"lim"(1)/(5^(n))(underset(r=1)overset(n)sum.^(n)C_(r)4^(r)-underset(r=1)overset(n)sum.^(n)C_(r)3^(r).)`
`= underset(nrarroo)"lim"(1)/(5^(n))(5^(n)-4^(n))= 1`
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