Observe the following pattern
\( (1 \times 2)+(2 \times 3)=\frac{2 \times 3 \times 4}{3} \)
\( (1 \times 2)+(2 \times 3)+(3 \times 4)=\frac{3 \times 4 \times 5}{3} \)
\( (1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)=\frac{4 \times 5 \times 6}{3} \)
and find the value of
\( (1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)+(5 \times 6) \)

Given:

\( (1 \times 2)+(2 \times 3)=\frac{2 \times 3 \times 4}{3} \)
\( (1 \times 2)+(2 \times 3)+(3 \times 4)=\frac{3 \times 4 \times 5}{3} \)
\( (1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)=\frac{4 \times 5 \times 6}{3} \)

To do:

We have to find the value of \( (1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)+(5 \times 6) \).

Solution:

We observe that,

\( (1 \times 2)+(2 \times 3)=\frac{2 \times 3 \times 4}{3} \)
\( (1 \times 2)+(2 \times 3)+(3 \times 4)=\frac{3 \times 4 \times 5}{3} \)
\( (1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)=\frac{4 \times 5 \times 6}{3} \)
Therefore,

$(1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)+(5 \times 6)=\frac{5\times6\times7}{3}$

$=5\times2\times7$

$=70$

Tutorialspoint

Updated on: 10-Oct-2022

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