2.3+3.4+4.5+---upto n terms =n ( n^2 +6n +11)/3
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n(n2 + 6n + 11)/ 3
.
Since S(1) = 2.3 = (1)(1 + 6 + 11)/3 = 6
n = 1
= k
i.e., S(k) = 2.3 + 3.4 +...+ (k + 1)
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