1+2+3+............+n<1/8(2n+1) ^2
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Answered by
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Step-by-step explanation:
lim
n→∞
1+
3
1
+
3
2
1
+.....+
3
n
1
1+
2
1
+
4
1
+.....+
2
n
1
=lim
n→∞
1−
3
1
1(1−
3
n
1
)
1−
2
1
1(1−
2
n
1
)
=lim
n→∞
3(1−
3
n
1
)
4(1−
2
n
1
)
=
3
4
Therefore,
lim
n→∞
1+
3
1
+
3
2
1
+.....+
3
n
1
1+
2
1
+
4
1
+.....+
2
n
1
=
3
4
Hence the correct answer is
3
4
.
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