Question

1+2+3+............+n<1/8(2n+1) ^2​

Answer 1

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

.