a. Notice that
1/(1*2) = 1/2 = 1 - 1/2
1/(2*3) = 1/6 = 1/2 - 1/3
1/(3*4) = 1/12 = 1/3 - 1/4
and so on, which suggests the n-th term of the sum can be written as
Then the sum itself is telescoping:
b. The proof is trivial:
so the formula found in (a) is correct.
Answer:
Option D.
Step-by-step explanation:
In the figure attached, Diagonals AC and BD are bisecting each other at a point P.
That means AP ≅ CP and DP ≅ BP
We have to prove : AB ≅ DC and AB ║ DC
Proof : In triangles BPA and CPD,
AP ≅ CP
DP ≅ BP
∠ APB ≅ ∠DPC [vertically opposite angles]
Therefore, by postulate SAS [Side-Angle-Side]
ΔBCP ≅ ΔCDP
Option D. will be the answer.
