Question

$1+\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+..........+\dfrac{1}{1+2+3+4+5+........n}$ Find the sum of series.​

Answer 1

ANSWER:

2n/(n+1)

GIVEN:

$1+\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+\\..........+\dfrac{1}{1+2+3+4+5+........n}$

TO FIND:

SUM OF THE SERIES

FORMULAE:

SUM OF n TERMS IN A SERIES = n(n+1)/2

AS THE TERMS ARE IN RECIPROCAL SUM = 2/n(n+1)

EXPLANATION:

SERIES = 2(1 - 1/2 +1/2 - 1/3+.....+1/n - 1/n+1)

This step is attained by substituting values from 1 to n

Also the consequtive terms cancel due to opposite sign.

NOTE : FULL EXPLANATION IN ATTACHMENT.

Answer 2

Answer:

ANSWER:

2n/(n+1)

GIVEN:

$\begin{gathered}1+\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+\\..........+\dfrac{1}{1+2+3+4+5+........n}\end{gathered}$

1+

1+2

1

+

1+2+3

1

+

1+2+3+4

1

+

..........+

1+2+3+4+5+........n

1

TO FIND:

SUM OF THE SERIES

FORMULAE:

SUM OF n TERMS IN A SERIES = n(n+1)/2

AS THE TERMS ARE IN RECIPROCAL SUM = 2/n(n+1)

EXPLANATION:

SERIES = 2(1 - 1/2 +1/2 - 1/3+.....+1/n - 1/n+1)

This step is attained by substituting values from 1 to n

Also the consequtive terms cancel due to opposite sign.

by the way my name is also same(Rishabh)