Question

question

1+1/1+2/1/1+2+3/+------ +1/1+2+3---- +n=2n/n+1

Answer 1

__see the attachment I hope it will help you^_^

From the principal of mathematical induction ,the statement P(n) is true for all nature Numbers n.

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#Nishu HaRyanvi ❤

Answer 2

Answer:

Hey Mate...

Step-by-step explanation:

Let P =  1 + 1 / 1 + 2 / 1 / 1 + 2 + 3 / +------ + 1 / 1 + 2 + 3 ---- + n = 2n / n + 1

For n = 1

L.H.S = 1

R.H.S =   2 ( 1 ) / ( 1 + 1 )  = 2 / ( 2 )

Hence L.H.S  =  R.H.S

P (n) is true for n = 1

Tn=1n (n+1 )2= 2n (n+1) =2 (n+1−n) n (n+1) = 2 [1n−1n+1]  

Thus -

T1 = 2 [11−12]

T2 = 2 [12−13]

T3 = 2 [13−14]

⋮

Tn = 2 [ 1n − 1n + 1]

Adding we get-

T1 + T2 + T3 … + Tn =2 [1 − 1n + 1]

Thus, Sum= 2n + 1

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