Question

What is the value of 1-2+3-4+5-.....+101

Answer 1

The value of 1 - 2 + 3 - 4 + 5 - 6 + ..... + 101 is "51".

Step-by-step explanation:

The given sequence are

1 - 2 + 3 - 4 + 5 - 6 + ..... + 101

S = (1 + 3 + 5 + ...... + 101) - (2 + 4 + 6 + 8 + ... + 100)    .....(1)

$S_{1}$ = 1 + 3 + 5 + ...... + 101

∴ First term(a) = 1, common differenc(d) = 3 - 2 = 2.

n = $\dfrac{101 - 1}{2} + 1 = 51$

∴ $S_{1}$ = $\dfrac{51}{2}\times (2(1) + (51 - 1)(2))$

= $\dfrac{51}{2}$ × 102

= 2601

Also,

$S_{1}$ = 2 + 4 + 6 + ...... + 100

∴ First term(a) = 1, common differenc(d) = 4 - 2 = 2.

n = $\dfrac{100 - 2}{2} + 2 = 50$

∴ $S_{2}$ = $\dfrac{50}{2}\times (2(2) + (50 - 1)(2))$

= 25 × 102

= 2550

∴ S = $S_{1}$ - $S_{2}$

= 2601 - 2550

= 51

Hence, the value of 1 - 2 + 3 - 4 + 5 - 6 + ..... + 101 is 51.

Answer 2

$1-2+3-4+5-\ldots+101=\\1+3+\ldots+101-(2+4+\ldots+100)=\\1+101+3+99+\ldots+49+53+51-(2+100+4+98+\ldots+50+52)=\\25\cdot102+51-(25\cdot102)=\\51$