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Permutations And Combinations
Prove that the sum to n terms of the series
11 + 103 + 1005 +........ is
Let Sn = 11 + 103 + 1005 + .......... up to n terms
= (10 + 1) + (100 + 3) + (1000 + 5) + ............... upto n terms
= [10 + 100 + 1000 + ..... upto n terms] + [1 + 3 + 5 + .......upto n terms]
= [10 + 102 + 103 + ....... upto n terms] + [ 1 + 3 + 5 +........... upto n terms]
Since the series in the first bracket is a G.P. series with first term 10, common ratio 10 and the
series in the second bracket is an A.P. series with first term 1 and common difference 2.
∴
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