Question

pls solve this special series.


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Answer 1

First let me make a general form for this series.

We see that,

• $\sf{a_1=2\times 3\times4=(1+1)(1+2)(1+3)}$

• $\sf{a_2=3\times 4\times 5=(2+1)(2+2)(2+3)}$

• $\sf{a_3=4\times 5\times 6=(3+1)(3+2)(3+3)}$

Thus the n'th term of the series is,

• $\sf{a_n=(n+1)(n+2)(n+3)}$

Hence the 50th term is,

• $\sf{\underline {\underline {a_{50}=(50+1)(50+2)(50+3)}}}$

• $\sf{\underline {\underline {a_{50}=51\times 52\times 53}}}$

• $\sf{\underline {\underline {a_{50}=140556}}}$

Answer 2

Answer:

50th term of series = 140556

Step-by-step explanation:

We are given with the following series;

2 * 3 * 4 + 3 * 4 * 5 + 4 * 5 * 6 + ..............

Firstly, we will try to write this series in general form;

Let $a_1$ = first term  ,   $a_2$ = second term and so on..

$a_1$ = 2 * 3 * 4 = (1 + 1) * (1 + 2) * (1 + 3)

$a_2$ = 3 * 4 * 5 = (2 + 1) * (2 + 2) * (2 + 3)

$a_3$ = 4 * 5 * 6 = (3 + 1) * (3 + 2) * (3 + 3)

And this will keep on going like this;

So, in general the nth term of the series is given by;

$a_n$ = (n + 1) * (n + 2) * (n + 3)

Hence, 50th term is given by;

$a_5_0$ = (50 + 1) * (50 + 2) * (50 + 3)

     = 51 * 52 * 53 = 140556

Therefore, 50th term of series = 140556 .