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Question

limn(1222+3242+52+....nterms)n2.

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Solution

S(1)=1
S(2)=14=(1+2)
S(3)=14+9=1+2+3
S(4)=14+916=(1+2+3+4) and so on
S(n)=(1)n+1(1+2+3+.....n)
(1)n+1n(n+1)2
limn(1)n+1(n+1)n
limn(1)n+12(1+1n)
limn(1)n+12 which is an indeterminate form.

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